Thanksgiving Thoughtful Thursday, More on Wally Smith and Voting Systems

I had some more thoughts on Dr. Smith's work on Range Voting, or more precisely:

As this is the first Thoughtful Thursday that will be on Thanksgiving, I close with a thanks to some of the wonderful people have explored the ideas of democracy. Political scientists study Locke but do not study Rosseua. I greatly enjoyed Dr. Smith's observations on the probabilities that face a single voter in an election, even a simple binary choice.

1. One goes into a voting booth. What are the odds that your vote will make a difference--that A would have won except for your vote for B. It is 3/sqrt(8*pi*V) where V is the number of voters. If there are a million voters, it one out 1671. Not bad. But this assumes that the poll says the election is a virtual dead heat. That every other voter is as likely to prefer A to B as the other way around, or it is simply "too close to call."
2. But many elections are that close. If the pollsters are saying that people are 60% for A and 40% for B, then the chances that your vote for B will make a difference are vanishingly small. (Even for a 51% to 49% case, the chances are about 10⁹⁰)
3. If we did not have any idea what other people thought--your electiont ou was too small to attract the interest of pollsters, then the odds that your vote would have an effect would be 1/V or (1/2V), depending upon whether V is even or odd. Thus, in our small-town Alderman election with a 1000 people, we would have about a one in 1500 chance of who votes.

Dr. Smith, with his wonderful wry humor, points out that in most elections it is not worth the voter's time to vote as their vote will never matter. And in spite of the hand-wringing of people complaining about voter apathy and lack of turn out, lots of people do vote. But on the other hand, people generally don't "waste their vote" on third party candidates that have even less of a chance than A or B. I can understand people not voting for Nader in the election of Bush vs. Gore, where it was close. But in the election of McCain vs. Obama, where it was clear who was going to win the Presidency, why did we not see more small party voters. As Dr. Smith pointed out that "rational voter" arguments should be given as much credit as most economists talking about a rational homo economicus.

The latter is the key assumption in Dr. Smith's work on Range Voting. Each voter looks at the poll data, and looks at the winner and closest runner up. Then,the voter decides which vote under the voting system, will he be most likely to affect.

And he gets the following algorithms for the Borda vote (a voter ranks the candidates adn the winner gets the sum of the ranks) and range voting.

Borda:: Look at the top two candidates in the polls. Award c votes to your favore. Award 0 votes to your second favorite. Now look at the third most likely to win (from poll data), if you think they are better than the average of the two previous candidates, give them c-2 votes. Otherwise give them 2 votes.

Range: Assume the maximum range you can assign is +1 and the minimum is -1 in this election. Go to the top two candidates, most likely to win--call them A and B. Decide which one you like the best out of those two, the lesser of two evils. Give them +1 to your favorite candidate and -1 to the worse of the two evils. Consult the poll data again and go to the third most likely to win. Call them C Give +1 if that candidates is better than the the average of candidates A and B, -1 otherwise. Then in deciding among the fourth most likely to win, if you like them better than the average of A, B and C, give them +1 , otherwise -1. Dr. Smith calls this generalization the Moving Average Strategy

Dr. Smith tries thirty voting system/strategy pairs. but all the strategic voting possibilities are individual strategies.

Let's say seven percent of the population follows the edicts of Demagogue C. the demagouge has considerable resources and hires computer boffins to determine the best strategic choice. Demagouge says give the vector <0.3,0.2, 0.8, 0.1> In a game theory setting, there might be another demagouge or interest group followed by five per cent that say give the vector< 0.6, 0.2,0.3,0.7> The other 88% are honest. Dr. Smith mentions the issue of allowing the honest voters to be honest which range voting does, and even ten percent honest voters will give better results for society than if everyone is strategic.

Coalitions are important. The wonderful paper of Vinent Conitzy, Tuomas Sandholm and Jerome Lang in Journal of Acm, volume 54, Issue Three discusses these--a topic for another Thoughtful Thursday. And as Dr. Conitzy pointed out, coalitions are weighted electoins. We may have these in shareholder elections where each vote is weighted by the number of shares that one has.

Thus, we should simulate it as a game. This means that each voter considers more possibilities than that given by the affine space and whether it makes sense to only look at the top two candidates in the polls.

I raise a possibility for elections to bodies like the house or Senate. The election is for m candidates over the n fielded. Each of the m winners are weighted by the number of votes they get. So in the Senatorial electon for State S, assume the Republican candiate, R gets 73% of the vote and the DemocratD gets 23% of the vote. There are two possibilities. Unlike the United States current system, the senators from each State are elected at the same time. R gets 1.46 votes and D gets 0.46 votes in the Sentate. The State loses 0.08 votes (for the minor parties). An alternative system which would be kinder to those voting for minor parties would be dividing by the number of votes for the top two candidates. Thus, here R would get 1.52 votes and B would get 0.48 votes so S would not lose a vote.

We should be thankful for the power of simulatoins to look at how large number of voters behavior under various models, and various possible voting systems. Dr. Smith is one such example. We should be thankful for the theoretical models that tells us that it is impossible to create elections and designing systeems that have certain properties. We should be thankful that there have been some trials of particapatory approaches, most notably Switzerland for referenda and cantonal democracy, Participatory Budgeting most notably in Brazil and to a lesser extent in south America, and Athenian Democracy And we should be thankful that somebody has asked in a survey-kind of way about participatory and direct democracy.

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