Voting Theory Part II:

1. Solutions Voting Theory Part II:

2. Proposed Solutions • Approval Voting • Range Voting • Instant Runoff Voting • Borda Count Modifications • Borda Preferendum • Quota Borda Count • Matrix Vote • Non-vote-centric solutions

3. Approval Voting • For each candidate, each individual voter either indicates approval, or doesn't • Voters can choose multiple candidates • Chosen candidates are not ranked • Just like Plurality Voting, but without the limitation to one choice • The candidate with the highest approval rating wins

4. Approval Voting • Approval Voting falls outside the scope of Arrow's Theorem, because the input is not individual preference rankings • Approval Voting avoids Arrow problems by restricting the domain (inputs) to simple partitions of the candidate set

5. Approval Voting • Advantages of Approval Voting • No Vote Splitting or spoiler effects • Simpler than ranking all the candidates • More informative than Plurality Voting • Permits voters to express their preferences more fully, e.g. indicating approval of third party candidates • Does not reward dishonesty

6. Approval Voting • Problems with Approval Voting: • If everyone indicates approval of third party candidates on the assumption that those candidates won't win, those candidates might win, even when most people would really prefer someone else • Violates “reverse symmetry” - two individuals with opposite preferences do not cancel • Can violate IIA

7. Approval Voting • Problems with Approval Voting: • Some say that determining the level of approval needed to warrant a vote is difficult • There are concerns that people will vote whimsically • People could also vote strategically, based on information from opinion polls

8. Range Voting • Commonly used for product evaluations, internet polls, etc. (Amazon product ratings, movie evaluations) • Individuals assign to each candidate a number from a specified range, with higher numbers being better • The candidate with the highest average wins

9. Range Voting • Range Voting already in use: Voting on Books • Some real work towards establishing Range Voting in US politics: http://www.rangevote.net/ http://rangevoting.org/

10. Range Voting • Range Voting falls outside the scope of Arrow's Theorem, because the input is not simply individuals' preference rankings • Range Voting avoids the problems of Arrow by gathering extra information (i.e. how much candidates are preferred compared to others on the scale)

11. Range Voting • Benefits of Range Voting: • Many people are familiar with it, and this will become truer as more people begin to use the internet • More expressive than Approval Voting, Plurality Voting, the Borda Count … • No Vote Splitting or IIA violations • Individual exaggerations have a small long-run impact

12. Range Voting • Criticisms of Range Voting: • Dishonesty pays – the best strategy is to give your favorite the maximum score, their competitor the minimum score, and so forth • Some worry that educating the public on the new system would be difficult

13. Instant Runoff Voting (IRV) • Voters rank candidates; if a candidate has a majority of 1st place votes, they win • If not, the candidate with the fewest 1st place votes is eliminated, and those ballots count towards the 2nd choice candidate • This continues until a candidate earns a majority of ballots

14. Instant Runoff Voting • Advocates of IRV are hard at work right now, and meeting with success: http://www.fairvote.org/instant-runoff-voting/

15. Instant Runoff Voting • Advantages of IRV: • Avoids Vote Splitting • Does not reward dishonesty

16. Instant Runoff Voting • Drawbacks to IRV: • The “center squeeze” - since so much emphasis is placed on 1st place rankings, a moderate candidate with broad approval is likely to get many 2nd place rankings and be eliminated in favor of more extreme candidates

17. Instant Runoff Voting • Drawbacks to IRV: • The “winner turns loser paradox” - a candidate can lose by being ranked higher! • How could that happen? • Suppose a liberal candidate takes votes from a conservative, with a moderate in the race • If this transfer causes that conservative candidate to lose, their votes will be transferred to the moderate, who may win • The liberal would have been happier to keep the conservative in the race, and let them keep those votes

18. Instant Runoff Voting • Drawbacks to IRV cont. • Must wait for all ballots to be collected and recorded to start calculating the winner, which would delay election results • When there are many candidates as well, the whole process is time consuming for voter and calculator

19. The Borda Count • Recall the standard Borda Count: Voters rank all the candidates, rank numbers are converted to points, and the candidate with the fewest points wins • The Borda Count had some problems: • Dishonesty pays • Violates IIA

20. The Borda Count • Some Borda Count advocates have tried to improve the system in various ways, and argue that Borda is superior to the other proposals: http://www.deborda.org/ • Improvements include embedding Borda voting in a multi-part discussion process

21. Non-Vote-Centric Solutions • More generally, broadening democratic participation beyond voting solves many problems. • Voters who have previously deliberated may be: • More civic-minded, less selfish voters • Better informed and more rational, e.g. single-peaked preferences • Hence, able to avoid Arrow's Theorem in some cases

22. Non-Vote-Centric Solutions • Deliberative polling also has benefits beyond the ballot box: • Results can be given to representatives, and perhaps taken more seriously than non-deliberative polls or petitions • Deliberative experience may promote critical thinking, citizenship and community

23. Other Solutions • Electoral reform to embrace third party candidates, reduce gerrymandering, etc. could improve the voting experience independent of changes in how we vote • Voting may be less degenerate, and deliberation more practical, on a smaller scale, e.g. with focus on specific community issues, greater individual impact, less special interest money, more sense of shared interests