Top

Social Choice and Welfare

10-12-2022 | Original Paper

Voting behavior in one-shot and iterative multiple referenda

Authors: Umberto Grandi, Jérôme Lang, Ali I. Ozkes, Stéphane Airiau

Published in: Social Choice and Welfare

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

We consider a set of voters making a collective decision via simultaneous vote on two binary issues. Voters’ preferences are captured by payoffs assigned to combinations of outcomes for each issue and they can be nonseparable: a voter’s preference over an issue might be dependent on the other issue. When the collective decision in this context is reached by voting on both issues at the same time, multiple election paradoxes may arise, as studied extensively in the theoretical literature. In this paper we pursue an experimental approach and investigate the impact of iterative voting, in which groups deliberate by repeating the voting process until a final outcome is reached. Our results from experiments run in the lab show that voters tend to have an optimistic rather than a pessimistic behaviour when casting a vote on a non-separable issue and that iterated voting may in fact improve the social outcome. We provide the first comprehensive empirical analysis of individual and collective behavior in the multiple referendum setting.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

For a survey, see Meir (2017); note that a number of papers have appeared since then. We survey the related literature in iterative voting in Sect. 2.2.

Examples from the real world are ubiquitous, including the commonly cited decision-making processes in Switzerland and California. For the latter, for instance, see: https://ballotpedia.org/California_2020_ballot_propositions.

Paradoxes arise even if voters have separable preferences, as pointed out by Benoît and Kornhauser (2010) as well as by Özkal-Sanver and Sanver (2006).

On the other hand, iterated bargaining has a longer history, and has been studied experimentally: especially, Diermeier and Morton (2005) test the well-known Baron–Ferejohn legislative bargaining model, by having subjects playing in several rounds until they agree on a proposal; although the iterated games in legislative bargaining and multiple referenda share some similarities, the nature of decisions (proposal by a single agent vs. voting), of the payoff (part of the proposal vs. associated with alternatives) and the underlying epistemic assumption (complete vs. partial knowledge) make however these two models quite different.

If \(\succ\) is a linear order then (\(TR \succ TL\) if and only if \(BR \succ BL\)) implies (\(TL \succ TR\) if and only if \(BL \succ BR\)).

The restriction to two variables is crucial: counting the number of separable preferences is an open problem (Hodge 2006).

If two half rational voters have the preference relation \(TR \succ TL \succ BR \succ BL\), it makes sense to distinguish further between one who votes for L and one who votes for B—the latter being perhaps more irrational than the former—but we will neglect this distinction.

Note that it is not necessary to write \({\text{ Col }}\)-optimistic, \({\text{ Row }}\)-optimistic, and so on, because there is only one variable for which this distinction applied; the other variable is separable.

In elections with 5 voters (Profiles 8 and 9), one subject among the 21 present in the lab is randomly chosen to wait through the election.

Another interest of Profile 7 is that if the current outcome is BR, and if the margins of victory for both B and R are large, then voters 1–6 would feel that their probability of being pivotal at the next stage is low for each of both issues, and may be tempted to vote TL to try to be pivotal in either one them (the probability of being pivotal on both being negligible); such a behaviour has been analyzed theoretically by Ahn and Oliveros (2012).

We mention studies by Laury (2005) and Baltussen et al. (2012) that found no difference between pay-one and pay-all designs. We chose a pay-all design to avoid adding a level of complication to the understanding of the instructions, and we believe that the effect of this choice is negligible given the small number of elections played by each user.

The binomial test yields significant difference at 5% from random choice for any value under 27 (62) for both (one of the) issues, given 147 choices. Thus, all values in Tables 9 and 10 regarding Profile 1, for instance, are statistically significantly different than random choice.

Note that this finding is based only on first stages of profiles 5–9, since there are no voters with semi-separable preferences in profiles 1–4.

One of the authors gave many talks for over a decade about multiple referenda in which the audience was presented with a two-issue example with ordinal preferences to make a choice (in a non-repeated setting). In this pseudo-experiments, an important difference pertained to that voters’ preferences were common knowledge. There was (almost) always a majority of optimists (about two-thirds) with a significant minority of pessimists.

We thank one of the reviewers for pointing this to us, which led us to add the discussion that follows.

We also note that both interpretations (optimistic/pessimistic, risk seeker/adverse) make more sense as plausible explanations when the expected payoffs of the concerned lotteries are equal or almost equal. While a voter preferring a lottery with possible payoffs 0 and 4 against one with possible payoffs 2 and 3 is definitely optimistic (or risk-seeking), one with the opposite preference perhaps simply applies the principle of insufficient reason (that is, assign probability \(\frac{1}{2}\) to each outcome in each lottery) and maximises expected payoff, rather than being pessimistic stricto sensu.

We thank one of the reviewers for this remark.

The choices in Profiles 2 and 4 cannot be compared with choices by any other voter in an iterated profile.

The estimation is restricted to fully separable and fully non-separable preferences. Semi-separable cases are analyzed in the sequel.

\(\text {Prob}[\varDelta x_{it}=1|SEP=0,PIV=0]-\text {Prob}[\varDelta x_{it}=1|SEP=1,PIV=0]=34.52--27.63\%\approx 6.9\%\).

Still, there are a significant number of subjects that change their votes, without however changing the result of the election. A fine-grained analysis of this can be found in Appendix 1.

Note that this slightly contrasts with the measure used by Bowman et al. (2014), who computes the social welfare as the Borda score of the election outcome divided by the number of voters. The two measures differ only on profiles with utility scales that are not linear.

Figure 8 in Appendix A shows the differences between the average social welfare and minimum possible social welfare as a percentage of the range of possible values in the first and last stages of profiles 5–8.

Recall that our findings in Section 5 show that there is no statistical difference between voters’ behaviour in one-shot elections and first stages of iterated elections, thus we can assume that the social welfare in the first stage is the same as if the election was held as one-shot.

Detailed comparative analysis regarding the “static” and “dynamic” groups can be found in the Appendix 1. Note also that Profiles 8 and 9 do not have a very large span of social welfare between the minimum and maximum attainable outcomes, as can be seen in the Table 18 in the Appendix 1.

No definitive conclusion can be drawn from these numbers, as most of our profiles were chosen so as to be at least somewhat pathological in the first place and not fit for this particular question.

Ahn DS, Oliveros S (2012) Combinatorial voting. Econometrica 80(1):89–141CrossRef

Airiau S, Grandi U, Perotto FS (2017) Learning agents for iterative voting. In: Proceedings of the 5th International Conference on Algorithmic Decision Theory (ADT). Springer, Cham, pp 139–152

Baltussen G, Post GT, Van Den Assem MJ, Wakker PP (2012) Random incentive systems in a dynamic choice experiment. Exp Econ 15(3):418–443CrossRef

Baumeister D, Selker A, Wilczynski A (2020) Manipulation of opinion polls to influence iterative elections. In: Proceedings of the 19th International Conference on Autonomous Agents and Multiagent Systems (AAMAS), pp 132–140

Benoît J, Kornhauser LA (2010) Only a dictatorship is efficient. Games Econ Behav 70(2):261–270CrossRef

Bowman C, Hodge JK, Yu A (2014) The potential of iterative voting to solve the separability problem in referendum elections. Theory Decis 77(1):111–124CrossRef

Bradley WJ, Hodge JK, Kilgour DM (2005) Separable discrete preferences. Math Soc Sci 49(3):335–353CrossRef

Brams SJ, Kilgour DM, Zwicker WS (1997) Voting on referenda: the separability problem and possible solutions. Elect Stud 16(3):359–377CrossRef

Brams SJ, Kilgour DM, Zwicker WS (1998) The paradox of multiple elections. Soc Choice Welf 15(2):211–236CrossRef

Brams SJ, Kilgour DM, Sanver MR (2007) A minimax procedure for electing committees. Public Choice 132(3):401–420CrossRef

Brânzei S, Caragiannis I, Morgenstern J, Procaccia AD (2013) How bad is selfish voting? In: Proceedings of the 27th AAAI Conference on Artificial Intelligence (AAAI), pp 138–144

Conitzer V, Lang J, Xia L (2011) Hypercubewise preference aggregation in multi-issue domains. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI), pp 158–163

Cornelio C, Pini MS, Rossi F, Venable KB (2019) Multi-agent soft constraint aggregation via sequential voting: theoretical and experimental results. Auton Agents Multi Agent Syst 33(1–2):159–191CrossRef

Çuhadaroğlu T, Lainé J (2012) Pareto efficiency in multiple referendum. Theory Decis 72(4):525–536CrossRef

Diermeier D, Morton R (2005) Experiments in majoritarian bargaining. In: Austen-Smith D, Duggan J (eds) Social choice and strategic decisions: essays in honor of Jeffrey S. Banks. Springer Berlin Heidelberg, Berlin, pp 201–226CrossRef

Elkind E, Grossi D, Shapiro E, Talmon N (2020) Egalitarian deliberative decision making. CoRR abs/2001.08031, https://arxiv.org/abs/2001.08031

Fain B, Goel A, Munagala K, Sakshuwong S (2017) Sequential deliberation for social choice. In: Proceedings of the 13th International Conference on Web and Internet Economics (WINE). Springer, Cham, pp 177–190

Fairstein R, Lauz A, Meir R, Gal K (2019) Modeling people’s voting behavior with poll information. In: Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems, AAMAS ’19, Montreal, QC, Canada, May 13–17, 2019, pp 1422–1430

Farnoud F, Yaakobi E, Touri B, Milenkovic O, Bruck J (2013) Building consensus via iterative voting. In: Proceedings of the 2013 IEEE International Symposium on information theory

Garg N, Kamble V, Goel A, Marn D, Munagala K (2019) Iterative local voting for collective decision-making in continuous spaces. J Artif Intell Res 64:315–355CrossRef

Goel A, Lee DT (2016) Towards large-scale deliberative decision-making: small groups and the importance of triads. In: Proceedings of the 2016 ACM Conference on Economics and Computation (EC), pp 287–303

Gonzales C, Perny P, Queiroz S (2008) Preference aggregation with graphical utility models. In: Proceedings of the 23rd AAAI Conference on Artifcial Intelligence (AAAI), pp 1037–1042

Grandi U, Loreggia A, Rossi F, Venable KB, Walsh T (2013) Restricted manipulation in iterative voting: condorcet efficiency and Borda score. In: Proceeding of the 3rd International Conference on Algorithmic Decision Theory (ADT). Springer, Berlin, Heidelberg, pp 181–192

Hodge JK (2006) Permutations of separable preference orders. Discrete Appl Math 154(10):1478–1499CrossRef

Hodge JK, Krines M, Lahr J (2009) Preseparable extensions of multidimensional preferences. Order 26(2):125–147CrossRef

Kavner J, Xia L (2021) Strategic behavior is bliss: iterative voting improves social welfare. Adv Neural Inf Proc Syst 34:19021–19032

Lacy D, Niou EMS (2000) A problem with referendums. J Theor Polit 12(1):5–31CrossRef

Laffont JJ (1987) Incentives and the allocation of public goods, chap 10. In: Alan J, Feldstein AM (ed) Handbook of public economics, vol 2. Elsevier, pp 537–569

Lang J, Xia L (2009) Sequential composition of voting rules in multi-issue domains. Math Soc Sci 57(3):304–324CrossRef

Lang J, Xia L (2016) Voting in combinatorial domains. In: Brandt F, Conitzer V, Endriss U, Lang J, Procaccia AD (Eds) Handbook of computational social choice. Cambridge University Press, pp 197–222CrossRef

Lang J, Mengin J, Xia L (2018) Voting on multi-issue domains with conditionally lexicographic preferences. Artif Intell 265:18–44CrossRef

Laury S (2005) Pay one or pay all: random selection of one choice for payment. Andrew Young School of Policy Studies Research Paper Series 06-13

Lev O, Rosenschein JS (2016) Convergence of iterative scoring rules. J Artif Intell Res 57:573–591CrossRef

Liekah L (2019) Multiagent reinforcement learning for iterative voting. Master’s thesis, Université Jean Monnet and Université Toulouse 1 Capitole, France

Meir R (2017) Iterative voting. In: Endriss U (ed) Trends in computational social choice. AI Access, pp 69–86

Meir R, Polukarov M, Rosenschein J, Jennings N (2010) Convergence to equilibria in plurality voting. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 24, no 1, pp 823–828

Meir R, Polukarov M, Rosenschein JS, Jennings NR (2017) Iterative voting and acyclic games. Artif Intell 252:100–122CrossRef

Meir R, Gal K, Tal M (2020) Strategic voting in the lab: compromise and leader bias behavior. Auton Agents Multi Agent Syst 34(1):31CrossRef

Obraztsova S, Markakis E, Polukarov M, Rabinovich Z, Jennings NR (2015) On the convergence of iterative voting: How restrictive should restricted dynamics be? In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 29, no 1

Özkal-Sanver I, Sanver MR (2006) Ensuring pareto optimality by referendum voting. Soc Choice Welf 27(1):211–219CrossRef

Powell O (2019) jtree—a Javascript toolbox for running economics experiments. Github https://opowell.github.io/jtree. Accessed 27 Oct 2022

Reijngoud A, Endriss U (2012) Voter response to iterated poll information. In: Proceedings of the 11th international conference on autonomous agents and multiagent systems, vol 2, pp 635–644

Van der Straeten K, Laslier J, Sauger N, Blais A (2010) Strategic, sincere, and heuristic voting under four election rules: an experimental study. Soc Choice Welf 35(3):435–472CrossRef

Wilczynski A (2019) Poll-confident voters in iterative voting. In: The 33rd AAAI Conference on Artificial Intelligence (AAAI), pp 2205–2212

Title: Voting behavior in one-shot and iterative multiple referenda
Authors: Umberto Grandi
Jérôme Lang
Ali I. Ozkes
Stéphane Airiau
Publication date: 10-12-2022
Publisher: Springer Berlin Heidelberg
Published in: Social Choice and Welfare
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-022-01436-0