I. INTRODUCTION

«Of importance when selecting a voting method is whether, on a regular basis, its outcomes accurately capture the intent of voters. A surprise is that very few procedures do this» (Saari 2023:357).

When considering elections and electoral systems, the prima facie supposition would be that they should be as neutral as possible. Nudging (‘N’ hereafter; Thaler and Sunstein 2008) would be the exact opposite of neutrality: even though its precise definition is debated (Congiu and Moscati 2022), there is a core element of steering behavior that cannot be neglected. On the one hand, ballot papers should not be designed to favor one option: a historically infamous case would be that of Adolf Hitler’s referendum in 1938^[1], where the positive option (Ja) is given the central position and a bigger symbol than the negative option (Nein). On the other, the literature on alternative voting methods shows that how people vote – and not what they vote for – could be improved. For instance, one voting method could encourage strategic voting whereas another more sincere choices.

The main way to access individuals’ political preferences is through their translation into votes, which is constrained by voting methods and electoral rules. Ballot papers reveal individuals’ choices, while their preferences are not directly observable (Baujard and Igersheim 2012): first, the design of a ballot could allow voters to express more or less information, thus filtering their preferences; second, strategic considerations could modify one’s preferences by adapting them to the beliefs regarding others’ expected behaviors; third, meta-rankings – i.e., individuals’ preferences over their own preferences – could be affected and steer the choice toward more individually or collectively oriented preferences, e.g., by supporting a candidate because of personal interest or by focusing on what would be collectively best. Compared to the most widespread voting design that allows voters to select one candidate, alternative methods could let voters provide more information, increase the psychic cost of strategic voting, and avoid forcing a tradeoff between individual and collective interests.

This work will explore the link between nudge theory and alternative voting methods, investigating whether a change in the design of the voting ballot could be justified as N. First, a review of the N definition will be crucial to understand whether a change in the voting design can be considered an instance of N. Second, changing the voting method will be analyzed in relation to two justifications of N applicable to liberal contexts. Third, empirical evidence will be reported to assess whether N is feasible in the context of voting methods.  

II. THE DEFINITION OF NUDGE

Since 2008 (Thaler and Sunstein 2008), N was proposed as a complementary behavioral tool to coercive laws. Nonetheless, its definition has been criticized under different aspects (Saghai 2013; Hansen 2016; Mongin and Cozic 2018): as there is no consensus on a unitary version, a review of the main positions will follow.

According to the original authors (Thaler and Sunstein 2008:5-6), a nudge is: «[1] Any aspect of the architecture of choices that alters [2] the behavior of individuals [3] in a predictable manner, [4] without prohibiting any option or significantly changing their economic incentives» with the purpose of «[5] influencing choices in a way that will make the choosers better off, as judged by themselves». It can be partitioned into different parts (Marsilio 2020): (1) the type of N, (2) the unit of interest, (3) the relationship with scientific evidence, (4) the conditions to be satisfied, and (5) the purpose of N.

A. Type of N

‘Any aspect’ could make N a ‘catch-all’ term. To avoid this, two main strategies focused on either (a) the mechanism triggered by N or (b) the type of N technique.

Triggered mechanism

First, the triggered mechanism relies on the psychological distinction – often referred to as ‘dual-process theory’ – between two ways in which humans process information (Kahneman 2011): System 1 – i.e., the fast and more intuitive way – and System 2, i.e., the slow and more reflective way. Three main positions could be endorsed by considering (a) only System-1 N, (b) only System-2 N, or (c) both systems adding other conditions. The first two options have been referred to as ‘narrow’ whereas the last one as ‘broad’ (Berthet and Ouvrard 2019). Some authors claimed that only System-1 influences should be deemed N (Bovens 2009; Marsilio forthcoming), with the additional difficulty of having to reply to ethical concerns regarding ‘slippery slopes’, threats to autonomy, and manipulation. Others tried to lean more toward System-2 N (Felsen, Castelo, and Reiner 2013; Sunstein 2016) to both take into account people’s attitudes toward N and avoid ethical controversies. Still others included both (Berthet and Ouvrard 2019) and other criteria – e.g., transparency (Hansen and Yespersen 2013), autonomy (Baldwin 2014), and heuristic triggering (Barton and Grüne-Yanoff 2015) – were proposed to distinguish between ethical and unethical N. Even though it is not possible to isolate one way of processing information, it could still be possible to either talk about the most likely triggered system by imagining a continuum between System 1 and 2 (Berthet and Ouvrard 2019) or assess which system the bias exploited by N is supposed to trigger based on empirical evidence, independently from what it actually triggers in the individuals when implemented (Marsilio forthcoming). The main advantage of focusing on the ‘intuitive’ aspect of N is to distinguish it from (a) providing more information and (b) boosting (Hertwig and Grüne-Yanoff 2017), i.e., another behavioral technique that aims to improve the long-term – and not short-term ones as in N – agent competencies through contextual education.

N technique

Second, the type of N can be distinguished in relation to (a) the field to which it applies (Szaszi et al. 2018) or (b) the technique used to alter the choice architecture (Münscher, Vetter, and Scheuerle 2016). The former (a) has the goal of shedding light on empirical studies concerning N effectiveness and its acceptance rate in surveys. Indeed, one important limitation of the empirical literature is that some studies are linked to a specific field – e.g., environmental N – and evidence on N effectiveness becomes tough to aggregate. Addressing the N field is also important to understand who is going to nudge (the nudger): private companies do alter the architecture of choices, although their goal usually concerns their own profit. Hence, marketing operations are not N (Congiu and Moscati 2022), and private companies may have to satisfy more conditions to ethically nudge consumers or employees (Ivanković and Engelen, 2022) as – unlike citizens – their preferences should never be presumed, e.g., based on civic duties. Thus, the field of N will be narrowed to public interventions. Moreover, N can be related to matters belonging to the public sphere or the private one: drawing a line between the two could be difficult; however, invading the private sphere would constitute a violation of one of the liberal hallmarks, first theorized by Mill (1859) through his harm principle and the legitimization of state interference with citizens’ freedom to avoid that they harm others. Thus, if N has to be implemented in a liberal context, it should merely concern the public sphere.

The latter (b) concerns more nuanced aspects of how decisions can be altered (Congiu and Moscati 2020). Nonetheless, it should be noted that any attempt to define N based on techniques is a form of ‘operationalization’, which presumes that at least the domain of N is shared a priori. Thus, a theoretical investigation of the concept of N could benefit more from the discussion on the mechanism triggered instead of the technique used.

B. Unit of Interest

‘The behavior of individuals’ refers to the unit that is to be nudged, which could be either (a) individuals or (b) groups.

Individuals

When considering individuals, it could be distinguished whether N refers to their behaviors – i.e., non-voluntary actions – and choices, i.e., the result of reflective thinking (Hansen and Yespersen 2013). However, it would be difficult to distinguish between altering choices and manipulation (White 2013). Thus, N should be referred to as altering behavior to avoid ethical controversies.

Groups

N could be related to groups in two ways: (1) as the unit of interest, where a nudge is in favor of a specific social group, e.g., to make exclusively poor people better off (Penders, Bauschke, and Guldemond 2019); (2) as the unit to be benefitted from the nudge – e.g., the poor – which could differ from the one being nudged, e.g., the rich (Hagman, Västfjäll, and Tinghög 2015). Considering the former, when assuming to operate at the public level, N one group and not the others could violate the normative value of equality as one group will be treated differently, e.g., only poor people will be given the psychological cost of a nudge. Moreover, it may raise concerns about violating people’s privacy to better target them (Kapsner and Sandfuchs 2015), e.g., a nudge becomes active based on people’s savings in their bank account. Considering the latter, it would not suit the N definition as those being nudged should be made better off, while the rich will not be better off if they are nudged to give away their personal wealth to the poor. Thus, the unit of interest will be assumed as ‘individual’.

C. Scientific Evidence

‘Predictability’ stems from scientific evidence, which can support N in two ways (Cartwright 2009): (a) the efficacy of the cognitive and behavioral features that N is based on and (b) the efficiency of N itself.

Efficacy

The former (a) derives from multidisciplinary studies of social and cognitive psychology, behavioral economics, and neurosciences (Asch 1951; Simon 1955; Tversky and Kahneman 1974; Berns et al. 2005) that have been showing systematic violations of the axioms of the neoclassical economic model of the homo oeconomicus (Von Neumann and Morgenstern 1947). These violations led to the discovery of biases that a nudger can exploit to conceive N. The corpus of evidence is so broad that critics may tackle one specific aspect at a single time (Gigerenzer 2015). In case a new N technique is implemented, it should be based on the efficacy of the mechanism that is supposed to be triggered.

Efficiency

The latter (b) derives from laboratory and on-field experiments that tested a variety of N techniques and showed their consequences to provide an a posteriori evaluation of the intervention. Even though it is difficult to aggregate these data, they can be useful to better understand a specific case or have a general grasp of N effectiveness through meta-analyses (Mertens et al. 2022). This aspect could be crucial in case the N justification relies on improving the efficiency of laws.

D. Conditions

‘Without prohibiting any option’ implies that N should satisfy the condition of reversibility (Saghai 2013), i.e., granting the possibility of doing otherwise compared to the option being nudged. This entails both that there is an opt-out option and that the nudge does not subvert humans’ decision-making faculties. Other conditions have been proposed: transparency (Hansen and Yespersen 2013), which implies that only transparent nudges should be justified; autonomy (Baldwin 2014), which implies that only those nudges that do not undermine autonomy should be justified; heuristic triggering (Barton and Grüne-Yanoff 2015), which implies that only nudges that do not exploit biases should be justified. Nonetheless, these conditions could severely limit the number of N techniques that could be used, possibly making one question their effectiveness.

Meta-level debate

The presence of conditions is also dependent on the level one wants to operate at, which could be either ethical (Bovens 2009) – referred to individuals – or political (Guala and Mittone 2015), referred to citizens. In the former case, one could wonder whether it is ethical to nudge either themselves or others. However, the most accurate framework to debate about N should be political when focusing on policymakers as nudgers in public institutions. In the latter, some political theories could be less demanding than others in terms of principles to satisfy compared to moral theories. In the context of political liberalism (Rawls 1993), it can be shown that reversibility is sufficient to reply to the criticisms of manipulation and threat to the agent’s autonomy (Marsilio forthcoming), with the debate occurring at a meta-level (Sumner 1996), i.e., beyond N in relation to the role of habits and the possibility of overriding them through practical reasoning. Thus, the elegance of the theory would benefit from just reversibility instead of adding other restrictions.

Considering incentives, the specification could be discarded: first, financial incentives are not N since choosing to save money would not be considered a bias; second, small – even non-financial – incentives can become N, e.g., when changing the framing of an incentive in terms of gains or losses.

E. Purpose

‘Make choosers better off’ is an instance of paternalism (Dworkin 2002). Two major streams can be found in the literature: (a) classic paternalism (Feinberg 1984) – i.e., an authoritarian figure decides what is in the best interest of a subordinate figure – and (b) libertarian paternalism (Sunstein and Thaler 2003), i.e., a subject is helped achieve one goal while preserving the freedom of choosing that goal. One of the most important distinctions between the two occurs at the level of means and ends (Sunstein 2014): libertarian paternalism is coextensive to the means one, while classic paternalism could be applied to means, ends, or both. N seems to belong to means paternalism: it influences the means to obtain a certain objective, although people endorsing different goals can still do otherwise. However, it could also be an instance of classic paternalism people’s preferences were presumed and not revealed. Thus, the purpose of N is strictly connected to its justification.

F. Justification

To justify N, three main arguments are found in the literature (Mongin and Cozic 2018): (a) inevitability, when a decision has to be made about how to set a default rule; (b) welfare, when an intervention instrumentally exploits rationality failures; (c) rationality, when an intervention aims to contrast rationality failures.

Inevitability

The first justification (a) is weaker as it can be applied to just a few N techniques and neglects the intentionality of N (Barton and Grüne-Yanoff 2015), along with the accountability that derives from it (Hansen 2016). If a policymaker was forced to nudge, they could claim a minor sense of responsibility compared to another policymaker who deliberately nudged.

Welfare

The second justification (b) is linked to the theory of well-being endorsed (Crisp 2017): (1) hedonism, (2) desire-satisfaction, or (3) objective-list theories. Instrumentally taking advantage of rationality failures implies that there is a goal – independent from rationality – to pursue. If people are to be made ‘better off’, a justification based on welfare seems the most central to the N account. The first type of theory (1) reduces human beings to their perceptual-emotive component. However, assuming to operate at the public level immediately places the discussion beyond pleasure and pain as they are difficult to measure and compare. The second (2) would aim to quantitatively increase individual preferences’ satisfaction, i.e., if I have the desire of X, doing X would increase my well-being. However, the desire should be ‘self-regarding’ and not ‘other-regarding’: the latter could imply applying paternalism independently from people’s preferences since the aim would be to quantitatively maximize the general good. The third (3) would aim to qualitatively increase individual preferences’ satisfaction, e.g., X is an objective good, doing X would increase my well-being. However, objective-list theories face the problem of presuming people’s approval of each objective good in the list: individuals would be better off pursuing an objective good even if they do not support it. Thus, one remaining possibility would be to justify N as self-regarding desire-satisfaction.

Rationality

The third justification (c) is related to the conception of rationality endorsed (Viale 2018): (1) neoclassical, (2) bounded, or (3) ecological. Assuming neoclassical rationality (1) would entail that all deviations from this standard should be corrected. However, a justification of this type would lead to hard paternalism (Conly 2014), meaning that an intervention could aim to reestablish rationality even when no harm is involved and independently from people’s will. Assuming bounded rationality (2) would entail that some rationality failures would be considered part of human behavior, without the need of correcting them. Thus, this justification would not be applicable to N. Assuming ecological rationality (3) would entail that some rationality failures could actually be rationality features in the correct context. This justification would require educational efforts to target how and when heuristics could work and – given a more long-term approach compared to N – its promoters tried to differentiate it from N, identifying new techniques like boosting to suit the case (Hertwig and Grüne-Yanoff 2017). It should be noted that boosting and similar behavioral tools are not antithetical to N and could work as complementary. However, all justifications concerning rationality seem astray in the sense of either being non-applicable or leading to other types of intervention.

G. Assumptions

To eschew many challenges, one strategy could be to (a) narrow the type of N to System 1-triggering mechanisms, i.e., exploiting biases, (b) narrow the field to public N and the unit of interest to individuals, (c) limit the conditions to reversibility, and (d) limit the justification to an increase of welfare based on self-regarding desire-satisfaction. N would then be defined as «The attempt to alter those aspects of the choice architecture that predictably influence the individuals’ short-term behavior» (Marsilio forthcoming), and its purpose will depend on the fostered normative framework. Political liberalism could incorporate two purposes: classic paternalist nudging (‘CPN’) as a complementary measure to already justified laws by constitutional and liberal principles to improve their efficiency; libertarian paternalist nudging (‘LPN’) as a sui generis intervention based on democratic practices – e.g., surveys and referenda – that are based on the majority’s will to reduce the gap between intentions and actions.

It will now be addressed whether a change in the voting method could be included in this suggested definition.

III. VOTING METHODS

Electing representatives is a crucial aspect of democracy; however, there is not just one electoral system and all of them have different consequences. Electoral systems can be divided into two major components: (a) the voting method, i.e., the design through which a voter can cast a valid vote; (b) the electoral rule, i.e., the aggregative method used to count votes and elect the winner. The N aspect applies to the former, while the latter will not be addressed here.

A. Alternative Voting Methods

The most widespread voting design is to choose one party or candidate (uni-choice voting, ‘UV’), which allows voters to provide one preference[2]. The two main alternatives are ranked voting (‘RV’; Bowler and Grofman 2000) – which allows voters to provide the order of their preferences – and score voting (‘SV’; Poundstone 2008), which allows voters to provide the intensity of their preferences. By default, the design of alternative methods allows the expression of more information than UV. Under UV, it is possible to provide only one piece of information on political preferences – e.g., «I vote for A» – without other potentially relevant information, e.g., «I would also like to support B» and «I would like to show my contempt for C». Under RV and SV, instead, one preference is not exclusive: positively evaluating one candidate does not prevent positively evaluating others.

Voting problems

In the literature, some problems have been highlighted in relation to UV (Laslier 2019): (1) wasted votes, (2) vote splitting, and – typical of two-round electoral systems like the French one – (3) the squeezing effect. First, wasted votes (Downs 1957) are votes that do not contribute to either electing someone in majoritarian contexts or winning a seat in the Parliament in proportional contexts. If most voters prefer either candidate A or B, then casting a vote for C – a candidate with no chance of winning – would lead to a wasted vote. Second, vote splitting (Dasgupta and Maskin 2004) occurs when two similarly oriented candidates A and B ‘split’ votes with each other, thus reducing their chances of winning while increasing the chances that a dissimilar candidate C wins. Third, the squeezing effect (Laslier and Sanver 2010) occurs when the candidate that would have been selected by the majority in the second round does not pass the first round under UV.

To contrast these issues, much attention has been drawn to the study of alternative voting methods, with laboratory (e.g., Forsythe et al. 1993), ‘framed-field’[3] (e.g., Laslier 2004), and online experiments (e.g., Igersheim et al. 2022) to empirically test the consequences of these methods, their understandability, and voters’ behavior and satisfaction. UV effortlessly works when there are two alternative candidates (Condorcet 1785): voters should pick one of the two options and the one with the highest number of votes wins. As soon as the number of possible candidates is more than two, strategic voting becomes an option (Duverger 1954). Voters will tend to focus on viable candidates – i.e., those that have a chance of winning the election – even though they may have preferred another. Thus, the possibility of strategic voting causes a discrepancy between intentions – i.e., the voter’s preferences – and actions, i.e., the voter’s choice expressed in the ballot.

B. Nudge the Voting Method

The previously proposed strategy implied that two types of N were justified: (a) LPN and (b) CPN. In both LPN and CPN, the reversibility condition would be granted by alternative methods: it would still be possible to express a preference for only one candidate by using only the first ranking under RV or giving only one maximum evaluation under SV. Moreover, the intuitive aspect would concern the ‘default rule’, whose functioning would be based on instrumentally exploiting the sincerity bias (Spenkuch 2015), i.e., the tendency to vote sincerely even though there is a systematic incentive to vote strategically.

Libertarian Paternalist Nudging (LPN)

First, the gap between intentions and actions would juxtapose voting methods and LPN: if the majority expresses an intention – e.g., in surveys, people show positive attitudes toward donating organs – and fails to act accordingly – e.g., they do not actually donate – then an intervention to reduce that gap – e.g., increase the number of organ donors by considering people organ donors by default – could be a case of LPN. Applying LPN to voting methods would depend on empirical data on voters’ satisfaction: if the majority is not satisfied with their current method and wants to change it, then implementing an alternative design could become an instance of N. From a practical perspective, it should be noted that a change in the voting method may also be a constitutional – and not only an empirical – question. However, this work will not dive into that additional problem and future studies could help assess the contexts where a change in the voting method could be easier to obtain.

Classic Paternalist Nudging (CPN)

Second, there could be a case for CPN. Even though the voting method is not a ‘law’, it could still be considered a ‘default rule’ justified by democratic and constitutional principles whose efficiency could be improved. Granted that representative democracies want to represent citizens’ political preferences, a change in the design of the voting method could be an instance of CPN if it provides ‘fairer’ elections when more than two candidates are allowed to compete. In this case, UV would not be optimal in electing the winner: only if the probability of victory were equally distributed among candidates – e.g., 33% probability of winning in a three-candidate race – could the electoral competition be fair under UV. Otherwise, UV would lead to the overrepresentation of the most-likely-to-win candidates and underrepresentation of the least-likely-to-win ones (Rae 1971). This specifically happens because of strategic voting, with some voting rules inciting voters to foster strategic behaviors more than others (Lepelley and Merlin 2001). Thus, applying CPN to voting methods would depend once again on empirical data, this time concerning voters’ behavior under different rules.

C. Empirical Data

To answer the two empirical questions above, it is possible to analyze data on satisfaction with voting methods for LPN and the ones on strategic voting for CPN.

Satisfaction with voting methods

Data on satisfaction can be collected through: (1) questions on satisfaction with democracy; (2) laboratory experiments, simulating elections with fictional candidates; (3) referenda, when a different method has been proposed as an alternative compared to the status quo; (4) exit polls, where an election using an alternative method was held; (5) ‘framed-field’ experiments, where voters test alternative methods after voting officially; (6) online experiments, where voters test alternative methods online.

First, some scholars tried to show how RV – where implemented – could be linked to an increase in satisfaction with democracy (Farrell and McAllister 2006). However, this indirect measurement may not be particularly reliable: people could associate any meaning to the word ‘democracy’, without a necessary reference to voting methods.

Second, laboratory experiments may have a problem of external validity as both the ideal setting and the presence of monetary incentives could incentivize people to foster a different behavior than the one displayed in real elections (Igersheim et al. 2016).

Third, referenda[4] have been mostly conducted between UV and RV (Ballotpedia n.d.), with the only exception of two American cities where approval voting (‘AV’; Brams and Fishburn 1978) – i.e., a binary version of SV – was supported. Two referenda at the national level in New Zealand and the United Kingdom did not pass, along with those in two Canadian federal districts. On the other hand, the situation in the US is different: two out of three federal states, four out of seven counties, and 37 out of 42 cities approved of RV. However, it should be noted that some cities have historically adopted RV in the first half of the Twentieth century (Fain 2022), possibly displaying a familiarity bias (Heller 2021), i.e., approving of a change since the alternative has already been experienced. Moreover, other referenda asked about repealing the alternative method implemented: the majority was in favor of keeping RV in Ireland, Maine, Pierce County (WA), and two out of three American cities. Lastly, some referenda included multiple questions – of which one concerning the voting system – to be approved at once, possibly influencing the results in any direction.  

Fourth, exit polls and post-election surveys have been carried out in local and federal elections using RV (FairVote 2023). Most of them showed a high appreciation of RV; however, these results could depend on (a) self-selected samples, (b) the additional change to a proportional – instead of majoritarian – electoral rule in some contexts, (c) strategic considerations about how elections went in terms of one’s preferred candidate placement, and (d) scientific bias – i.e., the tendency to support what is perceived to be endorsed by researchers – given that organizations like FairVote publicly support RV.

Fifth, ‘framed-field’ experiments have been mostly conducted in France with SV alternatives (Baujard and Igersheim 2007; Baujard et al. 2014; Bouveret et al. 2019), using self-selected samples. All these studies showed that French voters are dissatisfied with their current system and would prefer alternative methods. The same also happened in online surveys based on voluntary participation (Bouveret et al. 2018). However, the absence of representative samples could make one question the reliability of these data as some strong correlations have been found between age, the candidate supported, and satisfaction (Marsilio and Baujard forthcoming). Moreover, questions on satisfaction were not consistent across the experiments as the question framings and the number of possible answers changed over the years.

Sixth, some online experiments using representative samples compared UV to: (a) both RV and SV in the US in 2016 (Igersheim et al. 2022) and in Italy in 2022 (Marsilio and Delemazure forthcoming); (b) just RV in the US in 2020 and in Austria, England, Ireland, and Sweden in 2021 (Blais et al. 2021; Blais, Plescia, and Sevi 2021). Contrary to experiments with non-representative samples, all these studies – except for Italy – showed a preference toward the status quo. However, as alternative methods varied both in terms of the type of family – i.e., ordinal or cardinal – and the specific conditions – e.g., the SV scale tested – it is difficult to discuss satisfaction in general. Thus, evidence should be evaluated case by case, addressing voter satisfaction in a specific country with a determined alternative in comparison with its peculiar UV version.

Strategic voting

The debate on rationality affected the voting literature in a parallel way compared to N. The neoclassical assumption (Downs 1957) would be that wasted votes count as ‘irrational’ and voters should act strategically by routing for the ‘least-worse’ option among the ones that have a chance of winning the election to maximize the ‘weight’ of their vote. As it may be impossible for an individual to directly influence the election outcome, different theories were proposed to avoid the counterintuitive conclusion that voting is ‘irrational’ tout court:

• ‘instrumental’, based on game theory and the consideration that, if each rational voter decides not to vote, then any voter could determine the outcome of the election by voting. The greater the number of voters that will rationally abstain, the more rational voting becomes (Riker and Ordeshook 1968);
• ‘expressive’, based on moral considerations such as the ‘imperative duty’ (Meehl 1977) or the ‘good habit’ (Blais and Young 1999) to vote. If the chance to influence elections is negligible, then energy spent on sophisticated voting is irrational, whereas voting to express a preference may be entirely rational;
• ‘mixed-utility’, where voters display a mixture of instrumental and expressive behavior (Fiorina 1976). In this case, the definition of ‘strategy’ becomes fuzzier. On the one hand, all votes could be deemed strategic in the sense that voters are motivated by an expectation that the collective result can be at least probabilistically influenced (Buchanan and Yoon 2006). On the other, sincere voting would not be strictly defined as the opposite of strategic voting as most voters could just sincerely prefer viable candidates (Stephenson, Aldrich, and Blais 2018).

Voting systems should minimize wasted votes as they could lead to non-representation and discourage voters from participating (Amy 2000). Relying on instrumental behaviors to avoid wasted votes would be both (1) an assumption of neoclassical rationality and (2) detrimental to the representation of parties that are not likely to win the elections (Riker 1982).

First, voters foster a mixture of both instrumental and expressive behavior and are not neatly categorizable as strategic or sincere (Bol, Blais, and Laslier 2018; Spenkuch 2018). On the one hand, there are low psychic costs to vote strategically under UV (Spenkuch 2015). On the other, time pressure increases sincere behavior under UV – showing a link between sincerity and System 1 – while it does not affect the rate under the tested alternative AV (Alós-Ferrer and Garagnani 2022). Furthermore, some voters value equality so much that they prefer fairer systems to the ones that would favor their own interests (Bol et al. 2023).

Second, since UV does not correctly represent voters’ preferences in multi-candidate elections, it may not be ideal to force two-candidate elections to make UV work: (a) the competition between only two opposing candidates could lead to a polarized society (Abramowitz and Saunders 2008); (b) the lower the number of candidates, the lower the turnout rate (Bol and Ivandic 2022). Thus, the solution could be more oriented toward improving the correct representation of candidates than limiting the party supply.

Strategic voting under alternative methods is shown in the context of mathematical analysis (Satterthwaite 1975) and laboratory experiments (Van der Straeten et al. 2010), although it is almost impossible to be strategic when the number of both information provided and voting subjects substantially increases (Blais et al. 2016). When comparing laboratory and ‘framed-field’ results, strategic voting happens more frequently in the first scenario, where voters have a monetary incentive to maximize the chances of influencing the election outcome (Igersheim et al. 2016). Based on experimental evidence on SV, voters expressed more nuanced political preferences by taking advantage of the whole spectrum of possibilities granted by the evaluative scale tested (Baujard et al. 2018; Baujard and Lebon 2022). Moreover, the evaluations obtained under SV were similar to those expressed in a control question, which asked for a ‘sincere evaluation’ of the candidates and was not meant to be an alternative voting procedure itself (Igersheim et al. 2022).

IV. CONCLUSIONS

Considering the literature on N, LPN and CPN were identified as a possibility of eschewing many problems in its justification when assuming to operate in the context of political liberalism. Considering the literature on voting methods, alternative designs to UV could avoid some phenomena like wasted votes. Rarely have N and voting methods been associated, though they both stem from sub-optimal observed behaviors compared to rationality assumptions. To assess whether alternative voting methods could be an instance of N, empirical evidence is crucial in relation to both voter satisfaction and strategic voting. To change the default design of the most widespread voting method, consensus on changing or dissatisfaction with the current method could have counted as LPN, while the possibility of improving the efficiency of the existing voting system could have counted as CPN.

At the moment of writing this paper, empirical evidence on satisfaction is mixed: only in some specific contexts could LPN be applied. The analysis of satisfaction should depend on a case-by-case analysis, which could focus on states as well as cities.

Considering CPN, increasing complexity in large electorates with alternative methods would lead to unrealistic computations for voters to be strategic: sincere voting would be nudged whereas wasted votes could be avoided by default. Changing the design would make sincere votes count without demanding unrealistic rational efforts. By allowing the expression of more information, the election results could be more representative of citizens’ will, granting a fairer electoral competition and better representing minorities in proportional systems.

Nonetheless, this study had some limitations in both directions: for LPN, the reasons for either satisfaction or dissatisfaction with the current method should be central as this matter should specifically concern the voting method and not the electoral system in general; for CPN, as in most cases voting methods are safeguarded by the state’s Constitution, the real path for a change may not be just to ‘nudge the voting method’. Lastly, the exact alternative to implement is debatable and it would require both normative and practical considerations. Future studies could deepen this proposal by addressing these issues.  

REFERENCES

Abramowitz, A. I., and K. L. Saunders. 2008. “Is Polarization a Myth?” Journal of Politics 70(2):542-555.

Alós-Ferrer, C., and M. Garagnani. 2022. “Voting Under Time Pressure.” Judgment and Decision Making 17(5):1072-1093.

Amy, D. J. 2000. Behind the Ballot Box: A Citizen’s Guide to Voting Systems. Westport, US: Praeger.

Asch, S. E. 1951. “Effects of Group Pressure upon the Modification and Distortion of Judgments.” Pp. 222-236 in Groups, Leadership, and Men edited by H. Guetzkow. Pittsburgh, US: Carnegie Press.

Baldwin, R. 2014. “From Regulation to Behaviour Change: Giving Nudge the Third Degree.” Modern Law Review 77(6):831-857.

Ballotpedia. N.d. “Ranked-Choice Voting (RCV).” Retrieved 30 September 2023 https://ballotpedia.org/Ranked-choice_voting_(RCV)  

Barton, A., and T. Grüne-Yanoff. 2015. “From Libertarian Paternalism to Nudging – and Beyond.” Review of Philosophy and Psychology 6(3):341-359.

Baujard, A., F. Gavrel, H. Igersheim, J. Laslier and I. Lebon. 2018. “How Voters use Grade Scales in Evaluative Voting.” European Journal of Political Economy 55:14-28.

Baujard, A., and Igersheim, H. 2007. “Expérimentation du vote par note et du vote par approbation lors de l’élection présidentielle française du 22 avril 2007”. Retrieved 30 September 2023 https://halshs.archives-ouvertes.fr/halshs-00337290

Baujard, A., and H. Igersheim. 2010. “Frame-Field Experiments on Approval Voting in the Political Context.” Pp. 357-396 in Handbook on Approval Voting edited by J. Laslier, and M. R. Sanver. Heidelberg, Germany: Springer.

Baujard, A., and H. Igersheim. 2012. “Reconstructing Preferences in a Voting Context: Some Clues from Experimental Data on Voting Rules.” Pp. 273-291 in Freedom and Happiness in Economic Thought and Philosophy: From Clash to Reconciliation edited by R. Ege, and H. Igersheim, H. London-New York, UK-US: Routledge.

Baujard, A., H. Igersheim, I. Lebon, F. Gavrel and J. Laslier. 2014. “Who’s Favored by Evaluative Voting? An Experiment Conducted during the 2012 French Presidential Election.” Electoral Studies 34:131-145.

Baujard, A., and I. Lebon. 2022. “Not-so-Strategic Voters: Evidence from an In Situ Experiment during the 2017 French Presidential Election.” Electoral Studies 76.

Berns, G. S., J. Chappelow, C. F. Zink, G. Pagnoni, M. E. Martin-Skurski and J. Richards. 2005. “Neurobiological Correlates of Social Conformity and Independence during Mental Rotation.” Biological Psychiatry 58(3):245-253.

Berthet, V., and B. Ouvrard. 2019. “Nudge: Towards a Consensus View?” Psychology and Cognitive Science 5(1):1-5.

Blais, A., C. Plescia, J. Högström and G. Péloquin-Skulski. 2021. “Do (Many) Voters Like Ranking?” Party Politics 27(6):1223-1228.

Blais, A., C. Plescia and S. Sevi. 2021. “Do People Want Smarter Ballots?” Research and Politics 8(4).

Blais, A., S. L. St-Vincent, J. Pilet and R. Treibich. 2016. “Voting Correctly in Lab Elections with Monetary Incentives: The Impact of District Magnitude.” Party Politics 22(4):544-551.

Blais, A., and R. Young. 1999. “Why do People Vote? An Experiment in Rationality.” Public Choice 99(1-2):39-55.

Bol, D., A. Blais, M. Coulombe, J. Laslier and J. Pilet. 2023. “Choosing an Electoral Rule: Values and Self-Interest in the Lab.” Journal of Economic Psychology 95.

Bol, D., A. Blais and J. Laslier. 2018. “A Mixed-Utility Theory of Vote Choice Regret.” Public Choice 176(3-4):461-478.

Bol, D., and R. Ivandic. 2022. “Does the Number of Candidates Increase Turnout? Causal Evidence from Two-Round Elections.” Political Behavior 44(4):2005-2026.

Bouveret, S., R. Blanch, A. Baujard, F. Durand, H. Igersheim, J. Lang, A. Laruelle, J. Laslier, I. Lebon and V. Merlin. 2018. “Voter Autrement 2017 for French Presidential Election: The Online Experiment.” Retrieved 30 September 2023 https://hal.archives-ouvertes.fr/hal-03223762/

Bouveret, S., R. Blanch, A. Baujard, F. Durand, H. Igersheim, J. Lang, A. Laruelle, J. Laslier, I. Lebon and V. Merlin. 2019. “Voter Autrement 2017 for French Presidential Election: The Data of the In Situ Experiments.” Retrieved 30 September 2023 https://halshs.archives-ouvertes.fr/halshs-02379941

Bovens, L. 2009. “The Ethics of Nudge.” Pp. 207-220 in Preference change. Approaches from Philosophy, Economics and Psychology edited by T. Grüne-Yanoff, and S. O. Hansson. Berlin-New York, Germany-US: Springer.

Bowler, S., and B. Grofman. 2000. Elections in Australia, Ireland, and Malta under the Single Transferable Vote: Reflections on an Embedded Institution. Ann Arbor, US: The University of Michigan Press.

Brams, S. J., and P. C. Fishburn. 1978. “Approval Voting.” American Political Science Review 72(3):831-847.

Buchanan, J. M., and Y. J. Yoon. 2006. “All Voting is Strategic.” Public Choice 129(1-2):159-167.

Cartwright, N. 2009. “Evidence-Based Policy: What’s to be done about Relevance?” Philosophical Studies 143(1):127-136.

Condorcet, N. C. 1785. Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix. Paris, France: Imprimerie Royale.

Congiu, L., and I. Moscati. 2020. “Message and Environment: A Framework for Nudges and Choice Architecture.” Behavioural Public Policy 4(1):71-87.

Congiu, L., and I. Moscati. 2022. “A Review of Nudges: Definitions, Justifications, Effectiveness.” Journal of Economic Surveys 36(1):188-213.

Conly, S. 2014. “Against Autonomy: Justifying Coercive Paternalism.” Journal of Medical Ethics 40(5):349.

Crisp, R. (2017). “Well-Being.” In The Stanford Encyclopedia of Philosophy (Winter 2021 Edition) edited by E. N. Zalta. Retrieved 30 September 2023 https://plato.stanford.edu/entries/well-being/

Dasgupta, P., and E. Maskin. 2004. “The Fairest Vote of All.” Scientific American 290(3):92-97.

Downs, A. 1957. An Economic Theory of Democracy. New York, US: Harper and Row.

Duverger, M. 1954. Political Parties: Their Organization and Activity in the Modern State. New York, US: Wiley.

Dworkin, G. 2002. “Paternalism.” In The Stanford Encyclopedia of Philosophy (Fall 2020 Edition) edited by E. N. Zalta. Retrieved 30 September 2023 https://plato.stanford.edu/archives/fall2020/entries/paternalism

Fain, H. 2022. “U.S. Elections and Ranked Choice Voting: An Early History, in Five Acts.” Rank the Vote. Retrieved 30 September 2023 https://rankthevote.us/us-elections-and-ranked-choice-voting-an-early-history/

FairVote. 2023. “Research and Data on RCV in Practice.” Retrieved 30 September 2023 https://fairvote.org/resources/data-on-rcv/

Farrell, D. M., and I. McAllister. 2006. “Voter Satisfaction and Electoral Systems: Does Preferential Voting in Candidate-Centred Systems Make a Difference?” European Journal of Political Research 45:723-749.

Feinberg, J. 1984. Harm to Others. New York, US: Oxford University Press.

Felsen, G., N. Castelo and P. B. Reiner. 2013. “Decisional Enhancement and Autonomy: Public Attitudes Towards Overt and Covert Nudges.” Judgment and Decision Making 8(3):202-213. 

Fiorina, M. P. 1976. “The Voting Decision: Instrumental and Expressive Aspects.” The Journal of Politics 38(2):390-413.

Forsythe, R., R. B. Myerson, T. A. Rietz and R. J. Weber. 1993. “An Experiment on Coordination in Multi-Candidate Elections: The Importance of Polls and Election Histories.” Social Choice and Welfare 10(3):223-247.

Gigerenzer, G. 2015. “On the Supposed Evidence for Libertarian Paternalism.” Review of Philosophy and Psychology 6(3):361-383.

Guala, F., and L. Mittone. 2015. “A Political Justification of Nudging.” Review of Philosophy and Psychology 6(3):385-395.

Hagman, W., D. Andersson, D. Västfjäll and G. Tinghög. 2015. “Public Views on Policies Involving Nudges.” Review of Philosophy and Psychology 6(3):439-453.

Hansen, P. G. 2016. “The Definition of Nudge and Libertarian Paternalism: Does the Hand Fit the Glove?” European Journal of Risk Regulation 7(1):155-174.

Hansen, P. G., and A. M. Jespersen. 2013. “Nudge and the Manipulation of Choice: A Framework for the Responsible use of the Nudge Approach to Behaviour Change in Public Policy.” European Journal of Risk Regulation 4(1):3-28.

Heller, A. L. 2021. “Public Support for Electoral Reform: The Role of Electoral System Experience.” Electoral Studies 72.

Hertwig, R., and T. Grüne-Yanoff. 2017. “Nudging and Boosting: Steering or Empowering Good Decisions.” Perspectives on Psychological Science 12(6):973-986.

Igersheim, H., A. Baujard, F. Gavrel, J. Laslier and I. Lebon. 2016. “Individual Behavior under Evaluative Voting: A Comparison between Laboratory and In Situ Experiments.” Pp. 257-269 in Voting Experiments edited by A. Blais, J. Laslier and K. van der Straeten. Cham, Switzerland: Springer.

Igersheim, H., F. Durand, A. Hamlin and J. Laslier. 2022. “Comparing Voting Methods: 2016 US Presidential Election.” European Journal of Political Economy 71.

Ivanković, V., and B. Engelen. 2022. “Market Nudges and Autonomy.” Economics & Philosophy:1-28.

Kahneman, D. 2011. Thinking, Fast and Slow. New York, US: Farrar, Straus and Giroux.

Kapsner, A., and B. Sandfuchs. 2015. “Nudging as a Threat to Privacy.” Review of Philosophy and Psychology 6(3):455-468.

Laslier, J. 2004. Le vote et la règle majoritaire. Analyse mathématique de la politique. Paris, France: CNRS Éditions.

Laslier, J. 2019. Voter autrement. Le recours à l’évaluation. Paris, France: Rue d’Ulm.

Laslier, J., and M. R. Sanver. 2010. “Introduction to the Handbook on Approval Voting.” Pp. 1-12 in Handbook on Approval Voting edited by J. Laslier, and M. R. Sanver, M. R. Heidelberg, Germany: Springer.

Lepelley, D., and V. Merlin. 2001. “Scoring Run-Off Paradoxes for Variable Electorates.” Economic Theory 17(1):53-80.

Marsilio, S. 2020. Architettare le Scelte. Riflessioni di Filosofia e Politica sulla Teoria dei Nudge. Rome, Italy: IF Press.

Marsilio, S. Forthcoming. “The Justification for Nudging: Two Types of Paternalism within Political Liberalism.” Under review.

Marsilio, S., and A. Baujard. Forthcoming. “Are Alternative Voting Methods Preferred to the Status Quo? The Impact of Power Position, Age, and Political Ideology on French Voter Satisfaction.” Under review.

Marsilio, S., and T. Delemazure. Forthcoming. “Lacking System Longevity and the Status Quo Bias: Older Italian Voters Prefer Alternative Voting Methods to Their Current System.” Under review.

Meehl, P. E. 1977. “The Selfish Voter Paradox and the Thrown-Away Vote Argument.” American Political Science Review 71(1):11-30.

Mill, J. S. 1859. On Liberty. London, UK: J. W. Parker and Son.

Mertens, S., M. Herberz, U. J. J. Hahnel and T. Brosch. 2022. “The Effectiveness of Nudging: A Meta-Analysis of Choice Architecture Interventions Across Behavioral Domains.” Proceedings of the National Academy of Sciences of the United States of America 119(1).

Mongin, P., and M. Cozic. 2018. “Rethinking Nudge: Not One but Three Concepts.” Behavioural Public Policy 2(1):107-124.

Münscher, R., M. Vetter and T. Scheuerle. 2016. “A Review and Taxonomy of Choice Architecture Techniques.” Journal of Behavioral Decision Making 29(5):511-524.

Penders, D., D. Bauschke and J. Guldemond. 2019. “Nudging People out of Poverty.” The Maastricht Journal of Liberal Arts 11:31-42.

Poundstone, W. 2008. Gaming the Vote. Why Elections Aren’t Fair (and What We Can Do about It). New York, US: Hill and Wang.

Rae, D. W. 1971. The Political Consequences of Electoral Laws (rev. ed.). New Haven, US: Yale University Press.

Rawls, J. 1993. Political Liberalism. New York, US: Columbia University Press.

Riker, W. H. 1982. “The Two-Party System and Duverger’s Law: An Essay on the History of Political Science.” The American Political Science Review 76(4):753-766.

Riker, W. H., and P. C. Ordeshook. 1968. “A Theory of the Calculus of Voting.” The American Political Science Review 62(1):25-42.

Saari, D. G. 2023. “Selecting a Voting Method: The Case for the Borda Count.” Constitutional Political Economy 34(3):357-366.

Saghai, Y. 2013. “Salvaging the Concept of Nudge.” Journal of Medical Ethics 39(8):487-493.

Satterthwaite, M. A. 1975. “Strategy-Proofness and Arrow’s Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions.” Journal of Economic Theory 10(2):187-217.

Simon, H. A. 1955. “A Behavioral Model of Rational Choice.” Quarterly Journal of Economics 69(1):99-118.

Spenkuch, J. L. 2015. “(Ir)rational voters?” Retrieved 30 September 2023 https://mpra.ub.uni-muenchen.de/60100/

Spenkuch, J. L. 2018. “Expressive Vs. Strategic Voters: An Empirical Assessment.” Journal of Public Economics 165:73-81.

Stephenson, L. B., J. H. Aldrich and A. Blais. 2018. The Many Faces of Strategic Voting: Tactical Behavior in Electoral Systems Around the World. Ann Arbor, US: University of Michigan Press.

Sumner, L. W. (1996). Welfare, Happiness, and Ethics. New York, US: Oxford University Press.

Sunstein, C. R. 2014. Why Nudge? The Politics of Libertarian Paternalism. New Haven, US: Yale University Press.

Sunstein, C. R. 2016. “People Prefer System 2 Nudges (Kind Of).” Duke Law Journal 66:121-168.

Sunstein, C. R., and R. H. Thaler. 2003. “Libertarian Paternalism is Not an Oxymoron.” University of Chicago Law Review 70(4):1159-1202.

Szaszi, B., A. Palinkas, B. Palfi, A. Szollosi and B. Aczel. 2018. “A Systematic Scoping Review of the Choice Architecture Movement: Toward Understanding When and Why Nudges Work.” Journal of Behavioral Decision Making 31(3):355-366.

Thaler, R. H., and C. R. Sunstein. 2008. Nudge. Improving Decisions about Health, Wealth, and Happiness. Yale, US: Yale University Press.

Tversky, A., and D. Kahneman. 1974. “Judgment Under Uncertainty: Heuristics and Biases.” Science 185(4157):1124-1131.

van der Straeten, K., J. Laslier, N. Sauger and A. Blais. 2010. “Strategic, Sincere, and Heuristic Voting Under Four Election Rules: An Experimental Study.” Social Choice and Welfare 35(3):435-472.

Viale, R. 2018. Oltre il Nudge. Libertà di Scelta, Felicità e Comportamento. Bologna, Italy: Il Mulino.

von Neumann, J., and O. Morgenstern. 1947. Theory of Games and Economic Behavior (2^nd ed.). Princeton, US: Princeton University Press.

White, M. D. 2013. The Manipulation of Choice. Ethics and Libertarian Paternalism. New York, US: Palgrave Macmillan.

[1] «Do you agree with the reunification of Austria with the German Reich that was enacted on 13 March 1938 and do you vote for the party of our leader Adolf Hitler?». Dan Ariely ironically called this ballot paper a ‘nudge’, see https://danariely.com/hitler-nudge/

[2] Voting designs that allow for the expression of other types of preferences for candidates within (or outside of) the selected party would still fall into this category as it would still be considered a limited amount of information on voters’ preferences.

[3] This term was fostered to describe a voting simulation in the closest environment as possible to the actual voting experience (Baujard and Igersheim 2010), e.g., in an official polling station after having voted on election day.

[4] Appendix 1 will summarize the evidence on referenda per country, federal state, county, and city about both approving and repealing alternative methods. 

APPENDIX 1

REFERENDA ON ALTERNATIVE VOTING METHODS

Referenda on alternative voting methods mostly concerned RV. The approval rate of RV in referenda is summarized based on countries (Table 1), Federal states and districts (Table 2), counties (Table 3), and cities (Table 4). Two cities were asked about AV and are reported separately in Table 5. Alphabetical and then chronological order will be followed. The reference is Ballotpedia (n.d.) unless specified otherwise.

Table 1. Referenda on RV (Country)

Note. Two out of two did not pass.

^aRoberts (2012). The non-binding referendum included two questions: one about keeping the current system and one about which alternative should be implemented in case of a change. The reported percentage refers to the latter, where two ordinal alternatives combined were not preferred to UV. Nonetheless, the majority (57.8%) did not want to change the method in the former.

^bMcGuinness and Hardacre (2011).

Table 2. Referenda on RV (Federal State/District)

Note. Two out of five passed.

^aElections BC (2009:20). This province previously used RV in the 1920s.

^b“2016 Prince Edward Island Electoral Reform Referendum” (n.d.). Voters could pick one among five voting systems.

Table 3. Referenda on RV (American County)

Note. Four out of seven passed. In Multnomah County (OR), it previously failed in 1998 (40.1%).

^aSmart Voter (1998)

^bClallam County (n.d.:13).

Table 4. Referenda on RV (American City)

Note. 37 out of 42 passed. In Fort Collins (CO), Ann Arbor (MI), and Burlington (VT), it initially passed, then it was repealed, and – as reported in the table – it passed again. In San Francisco, it previously failed in 1996 (43.6%). Aspen (CO) was not reported as it was repealed later. Cincinnati (OH) – where it failed three times in 1988, 1991, and 2008 – was not reported as the question concerned proportional representation and not the voting design.

^aCities that have historically adopted RV in the first half of the Twentieth century (Fain 2022).

^bSangamon County (2007).

^cMelanson (2019).

^dEugene (n.d.:42).

^eThe specific alternative was the object of a second question, which showed a preference for RV (75.8%) compared to AV (24.2%).

Table 5. Referenda on AV (American City)

Note. Two out of two passed.

Referenda about repealing the alternative method – all concerning RV – once implemented will be summarized based on countries (Table 6), Federal states (Table 7), counties (Table 8), and cities (Table 9). The reference is Ballotpedia (n.d.) unless specified otherwise.

Table 6. Referenda on Repealing RV (Country)

Note. One out of one did not repeal RV.

^aIreland Wiki (n.d.).

Table 7. Referenda on Repealing RV (American Federal State)

Note. One out of one did not repeal RV.

Table 8. Referenda on Repealing RV (American County)

Note. One out of one did not repeal RV.

Table 9. Referenda on Repealing RV (American City)

Note. Two out of three did not repeal RV. Cambridge (MA) – where RV was kept in 1965 – was not reported as the question concerned proportional representation and not the voting design.

REFERENCES

Ballotpedia. N.d. “Ranked-Choice Voting (RCV).” Retrieved 30 September 2023 https://ballotpedia.org/Ranked-choice_voting_(RCV) 

Clallam County. N.d. “11/6/2007. Amendment #1. Instant Run-Off Voting.” Charter Amendments. Retrieved 30 September 2023 https://www.clallamcountywa.gov/DocumentCenter/View/11470/Charter-Amendments?bidId=

Elections BC. 2009. “Statement of Votes. Referendum on Electoral Reform.” Retrieved 30 September 2023 https://elections.bc.ca/docs/rpt/2009Ref/2009-Ref-SOV.pdf

Eugene. N.d. “9/18/2001. Preference Voting for Mayor and City Councilor Elections.” Election Index. Retrieved 30 September 2023 https://www.eugene-or.gov/DocumentCenter/View/468/City-of-Eugene-Election-History?bidId=

Ireland Wiki. N.d. “Fourth Amendment of the Constitution Bill, 1968.” Retrieved 30 September 2023 https://eire.fandom.com/wiki/Fourth_Amendment_of_the_Constitution_Bill,_1968

McGuinness, F., and J. Hardacre. 2011. “Alternative Vote Referendum 2011.” House of Commons Library. Retrieved 30 September 2023 https://commonslibrary.parliament.uk/research-briefings/rp11-44/

Melanson, A. 2019. “Lowell Voters Favor Hybrid Election Model; Approve CPA.” The Sun. Retrieved 30 September 2023 https://www.lowellsun.com/2019/11/05/lowell-voters-favor-hybrid-election-model-approve-cpa/

Roberts, N. 2012. “Referendums – Consultative Referendums after 1990.” Te Ara – The Encyclopedia of New Zealand. Retrieved 30 September 2023 http://www.TeAra.govt.nz/en/graph/36957/results-of-the-1992-and-2011-indicative-referendums

Sangamon County. 2007. “City of Springfield. Change the Method of Electing Municipal Officers.” Retrieved 30 September 2023  https://countyclerk.sangamonil.gov/results/April%2017,%202007%20Consolidated/cumm.htm

Smart Voter (1998). “Measure F.” Retrieved 30 September 2023 http://www.smartvoter.org/1998nov/ca/scl/meas/F/

Wikipedia contributors. “2016 Prince Edward Island Electoral Reform Referendum.” Wikipedia, The Free Encyclopedia. Retrieved 30 September 2023 

https://en.wikipedia.org/w/index.php?title=2016_Prince_Edward_Island_electoral_reform_referendum&oldid=1148643896

Acknowledgments:

I would like to personally thank my supervisor Roberta Sala; Pierre-Etienne Vandamme, who provided useful feedback on two drafts of the paper; Herrade Igersheim and André Lapidus, who read and provided comments on my paper for the 24^th ESHET Summer School; Davide Battisti, with whom I had passionate discussions during lunches and ‘nudged’ me to both think more about the subject and write this paper; Petr Špecián – who organized the conference Fortifying Democracy for the Digital Age: Interdisciplinary Perspectives – and Ivan Jarabinský, Viktor Ivanković, and Andres Moles for their comments on my presentation there.