Practical Preferential Voting (Herrenhausen 2018)
A Theorist’s View onPractical PreferentialVoting RulesFelix BrandtMathematics and Politics: Democratic Decision MakingSchloss Herrenhausen, Hannover, May 2018
How to select a single alternative based on thepreferences of multiple voters?Practical Preferential Voting Rules!2Felix Brandt
Why Preferential Voting?How majority rule might have stopped Donald Trump (E. Maskin and A. Sen, New York Times, April 2016)Eric S. MaskinAmartya K. SenPractical Preferential Voting Rules!3Felix Brandt
Why Preferential Voting?How majority rule might have stopped Donald Trump (E. Maskin and A. Sen, New York Times, April 2016)‣is the worst choice according to a majority of voters.‣ If the preferences of all voters are reversed,still wins.‣‣loses all pairwise majority comparisons.wins all majority comparisons(Condorcet winner).‣ In a poll conducted among 22 leading socialchoice theorists at Chateau du Baffy (France)in 2010, Plurality received no support at all(among 18 voting rules).Practical Preferential Voting Rules!4Felix Brandt
Voting Rules Matter5432acbdeebcdadcbeabdeca‣ Pluralityused in US, Mexico, South Korea, ‣ Bordaused in Slovenia, at Harvard University, ESC, ‣ Schulzeused by Pirate Party, Wikipedia, Debian, ‣ Instant-runoffused in Canada, UK, Hollywood (Academy Awards), ‣ Plurality with runoffused in France, Brazil, Russia, Practical Preferential Voting Rules!5Felix Brandt
Voting Rules Matter5432acbdeebcdadcbeabdeca‣ Pluralityused in US, Mexico, South Korea, ‣ Bordaused in Slovenia, at Harvard University, ESC, ‣ Schulzeused by Pirate Party, Wikipedia, Debian, ‣ Instant-runoffused in Canada, UK, Hollywood (Academy Awards), ‣ Plurality with runoffused in France, Brazil, Russia, Practical Preferential Voting Rules!6Felix Brandt
Voting Rules Matter5432acbdeebcdadcbeabdeca‣ Pluralityused in US, Mexico, South Korea, ‣ Bordaused in Slovenia, at Harvard University, ESC, ‣ Schulzeused by Pirate Party, Wikipedia, Debian, ‣ Instant-runoffused in Canada, UK, Hollywood (Academy Awards), ‣ Plurality with runoffused in France, Brazil, Russia, Practical Preferential Voting Rules!7Felix Brandt
Voting Rules Matter5432acbdeebcdadcbeabdeca‣ Pluralityused in US, Mexico, South Korea, ‣ Bordaused in Slovenia, at Harvard University, ESC, ‣ Schulzeused by Pirate Party, Wikipedia, Debian, ‣ Instant-runoffused in Canada, UK, Hollywood (Academy Awards), ‣ Plurality with runoffused in France, Brazil, Russia, Practical Preferential Voting Rules!8Felix Brandt
Voting Rules Matter5432acbdeebcdadcbeabdeca‣ Pluralityused in US, Mexico, South Korea, ‣ Bordaused in Slovenia, at Harvard University, ESC, ‣ Schulzeused by Pirate Party, Wikipedia, Debian, ‣ Instant-runoffused in Canada, UK, Hollywood (Academy Awards), ‣ Plurality with runoffused in France, Brazil, Russia, Practical Preferential Voting Rules!9Felix Brandt
multi profilesingle profileD. Felsenthal (2018):On Paradoxes Afflicting Voting ProceduresPluralityBordaSchulzeIRVRunoffCondorcet winner paradox — Absolute majority paradox— ———Condorcet loser paradox ————Absolute loser paradox ————Pareto paradox—————Additional support paradox——— Reinforcement paradox—— No-Show paradox—— Twin paradox—— Subset choice paradox Preference inversion paradox —— Practical Preferential Voting Rules!10Felix Brandt
Three DesiderataVoting rules ‣ should not require strict, complete, or transitive preferences‣ Insistence on strict rankings impedes preferential rules.‣ Pairwise (aka “C2”) rules allow great input flexibility.‣ should satisfy desirable properties‣ e.g., Pareto-optimality, participation, reinforcement, ‣ even when preferences fail to be strict, complete, or transitive‣ should be simple and easy to compute‣ need not necessarily be easily comprehensible by general public‣ in particular, should allow for easy verification of resultPractical Preferential Voting Rules!11Felix Brandt
Condorcet Winners‣ Whenever Condorcet winners exist, all of these desiderata(plus strategyproofness) can be achieved by selecting theCondorcet winner.‣ In a vast majority of cases, Condorcet winners do exist!‣ Feld and Grofman (1992) analyze election data from 36 real-worldelections, all of which admitted a Condorcet winner.‣ Summarizing 37 empirical studies from 1955 to 2009, Gehrleinand Lepelley (2011) conclude that “there is a possibility thatCondorcet's Paradox might be observed, but that it probably isnot a widespread phenomenon.”‣ For 4 alternatives, the probability of a Condorcet winner is at least82% under the (unrealistic) impartial culture assumption.‣ For few alternatives, any Condorcet extension will do.Practical Preferential Voting Rules!12Felix Brandt
Maximal Lotteries‣ Randomized voting rule proposed byKreweras (1965) and Fishburn (1984)‣‣rediscovered by Laffond et al. (1993),Felsenthal and Machover (1992),Fisher and Ryan (1995), Rivest and Shen (2010)variants known as bipartisan set, essential set, andscrutin de Condorcet randomiséGermain Kreweras‣ Returns lotteries that are preferred to anyother lottery by an expected majority of votersPractical Preferential Voting Rules!13Peter C. FishburnFelix Brandt
Example5432acbdeebcdadcbeabdeca‣ Let Mx,y {i : x i y} - {i : y i x} .‣ A lottery p is maximal if pT M 0.‣ p is degenerate if and only if there is a (weak) Condorcet winner.‣ In contrast to Condorcet winners, maximal lotteries always exist.Practical Preferential Voting Rules!14Felix Brandt
Example5432acbdeebdcadcbeabdeca‣ Let Mx,y {i : x i y} - {i : y i x} .‣ A lottery p is maximal if pT M 0.‣ p is degenerate if and only if there is a (weak) Condorcet winner.‣ In contrast to Condorcet winners, maximal lotteries always exist.Practical Preferential Voting Rules!15Felix Brandt
orcet winner paradox — —Absolute majority paradox— ————Condorcet loser paradox —————Absolute loser paradox —————Pareto paradox——————Additional support paradox——— (—)Reinforcement paradox—— —No-Show paradox—— —Twin paradox—— —Subset choice paradox —Preference inversion paradox —— —multi profilesingle profileD. Felsenthal (2018):On Paradoxes Afflicting Voting ProceduresPractical Preferential Voting Rules!16Felix Brandt
Turning Impossibilities intoCharacterizations of Maximal Lotteries‣ Arrow’s impossibility (Arrow, 1951)‣ Brandl and B., Working paperKenneth J. Arrow‣ Reinforcement impossibility (Young & Levenglick, 1978)‣ Brandl, B., and Seedig, Econometrica (2016)H. Peyton Young‣ No-show paradox (Moulin, 1988)‣ Brandl, B., and Hofbauer, GEB (2018)Hervé MoulinPractical Preferential Voting Rules!17Felix Brandt
Degree of RandomizationMaximal Lottery Support Size (IAC)m .5%43.3%43.9%5.3%36.8%m 5%m 5Shannon Entropy (IAC)49.1%48.3%24.2%24.5%0.25m 21MaximalLotteriesm 1180.3%75.5%m 575.2%Plurality0.00n 5n 513n 5015112151151501nSize 1Size 3Size 5Size7Practical Preferential Voting Rules!18Felix Brandt
Challenges‣ Flexible and expressive specification of preferences‣ Educate users about randomization‣ Verifiable randomization[the maximal lotteries system] is not only theoreticallyinteresting and optimal, but simple to use in practice;it is probably easier to implement than, say, IRV.We feel that it can be recommended for practical use.Rivest and Shen (2010)voting.mlPractical Preferential Voting Rulespnyx.dss.in.tum.de!19votation.ovhFelix Brandt
References‣ Aziz, Brandl, B., and Brill. On the tradeoff between efficiency andstrategyproofness. Games and Economic Behavior, 110:1-18, 2018.‣ Brandl and B. Arrovian aggregation of convex preferences. Working paper.‣ Brandl, B., and Hofbauer. Welfare maximization entices participation.Games and Economic Behavior, forthcoming.‣ Brandl, B., and Seedig. Consistent probabilistic social choice.Econometrica, 84(5):1839-1880, 2016.‣ Brandl, B., and Stricker. An analytical and experimental comparison ofmaximal lottery schemes. IJCAI 2018.Practical Preferential Voting Rules!20Felix Brandt
Practical Preferential Voting Rules Felix Brandt Why Preferential Voting?!4 ‣ is the worst choice according to a majority of voters. ‣ If the preferences of all voters are reversed, still wins. ‣ loses all pairwise majority comparisons. ‣ wins all majority comparisons (Condorcet winner). ‣ In a poll conducted among 22 leading social .
All general voting places are open from 8 a.m. to 8 p.m. (Pacific time) on October 24, 2020. Electoral District Voting Place Name Voting Place Address Voting Place City Cariboo-Chilcotin St. Andrews United Church 1000 Huckvale Pl Williams Lake, BC Cariboo-Chilcotin Sulphorous Lake Comm Hall 7571 PettyJohn Rd Bridge Lake, BC .
Voting procedures have been formally studied in the game theory literatue under the name of voting games. Due to its real life importance, weighted majority voting games have received a lot of attention. In the literature on voting games, the members are called players. One of the basic questions is how
chanisms with a voting scheme closer to anti-plurality voting. By the latter condition, we manipulate the incen-tives for strategic manipulation. As we explain in Appendix A, standard game-theoretic reasoning predicts a re-duction in strategic voting as the intermediate score and prize increase (as the opportunity costs of sincere voting
Online voting is different from e-voting systems, in the way that, in ―Online Voting‖, the user can vote directly from home, using devices that are used in daily life, like, laptop, computers, whereas, in e-voting, the voter needs to go physically to the polling centre, where, he/she will be verified
In this thesis, we concentrate on the topic of strategic manipulation in voting sys-tems. Voting as an aggregating method is widely used in collective decision mak-ing and network design. Voting rules can show some undesirable behaviour such as being vulnerable to strategic manipulation. We first explain our voting setup in
The details of the voter, the pin used to vote and the time of voting is updated in a database table called "youhavevoted" This is to allow the system to check those who have voted so as to prevent double voting. The voting process is summarized in Figure 6. Start the Voting Application Admin Login Agent Login Voter Login Create User
Professor David Wagner, Chair Voting is the bridge between the governed and government. The last few years have brought a renewed focus onto the technology used in the voting process and a hunt for voting machines that engender confidence. Computerized voting systems bring imp roved usability and cost benefits but
discretion, the option to replace the Mini Wi-Fi Home Hotspot 500 Kit or any component thereof which is identified as faulty or below standard, or as a result of inferior workmanship or materials. Products over 28 days old from the date of purchase may be replaced with a refurbished or repaired product. The conditions of this guarantee are:
