Thanks once again to NCrissieB for the opportunity to address BPI.
Hugs to all who want them.
Today, I'll discuss:
- Why, when there are more than 2 candidates in a race, there is no perfect voting method
- Why plurality voting (the scheme we use) is really terrible
and
- Some better alternatives.
It's in part a re-post of a diary I did in April 2008, based on the book Gaming the Vote.
The book is Gaming the Vote by William Poundstone. The book is subtitled "Why Elections aren't fair, and what we can do about it".
It's an excellent book. Poundstone makes often abstruse arguments clear, without dumbing things down. He points out all sorts of interesting historical information - for instance, one person who was very interested in voting theory is Lewis Carroll.
This is not a book about hanging chads, fake votes, and things like that. Rather, it's about the problems of our current method of voting - called plurality voting - and some better alternatives. Plurality voting is the worst of all seriously considered schemes.
The first half of this book describes the problem - the spoiler effect - in great detail, going into the Nader effect in 2000 (so well known to us all) but also many other spoiled elections, old and new, national and local, and the efforts by the Democrats and Republicans to help third parties that they thought would hurt the other major party. Lots of interesting stuff here, but my main interest is in the second part, where Poundstone talks about various schemes for voting. For example, of elections for POTUS, five were probably decided by a third party: (1844, 1848, 1884, 1912, and 2000), and two others may have been (1892, 1992).
When there are only two candidates on the ballot, it doesn't matter what method is used, they all give the same result. But when there are more than two, even if the third, fourth, etc. attract only a few voters, then weird stuff happens. Arrow proved that no ranking system can avoid paradox, but later results have shown that in some systems, paradox is unlikely. the reason Nader hurt Gore is because we use the worst system: Plurality voting.
Here are some of the main systems. And hypotheses about what would have happened in 2000, using 200 hypothetical voters, and pretending there is direct election (doing this for each of 50 states is too involved for a diary, but the same ideas work).
Plurality voting, which we're all familiar with, is when you 'pick one' and vote. This leads to disaster. People who like Nader over Gore feel conflicted - do they vote for Nader, risking Bush? Do they vote for Gore, although they prefer Nader? Do they stay home? And Bush wins.
Approval voting is when you can vote for as many as you like. You pick all the candidates you approve of, and check their names. The big problem here is that you can't express degree of preference. If you LOVE Nader, LIKE Gore and HATE Bush, you have no way to express that. You can say Gore is the same as Nader (and approve them both) or Gore is like Bush (and approve only Nader).
Borda count is when you rank the candidates, from most to least preferred. Then, in (say) a four candidate race, every first place vote is worth 3 points, every second place vote is worth 2 points, every third place vote is worth 1 point, and every fourth place vote is worth 0. This is a very easy system to manipulate, and isn't preferred by any serious voting theorist. It's the scheme used in some sports polls, and has led to scandal. If people are honest it can still lead to paradox (although it isn't likely to do so), and it's very easy to game: Bush voters could rank Nader ahead of Gore; Gore voters could rank Buchanan ahead of Bush. But if people are honest, it's not bad.
Using the 2000 election, with Bush, Gore and Nader (to simplify a little) there are 6 possible ranks: BGN, BNG, GBN, GNB, NBG, NGB. Let's take a guess that people's preferences are:
BGN : 70 people
BNG : 10 people
GBN: 10 people
GNB: 70 people
NBG: 10 people
NGB: 30 people
these might not be exactly right, but it will work out the same anyway.
Bush gets 210 + 30 + 20 + 70 + 20 + 30 = 380
Gore gets 140 + 10 + 30 + 210 + 10 + 60 = 460
Nader gets 70 + 20 + 10 + 140 + 30 + 90 = 360
Gore wins, and Nader voters get to vote for Nader, and people learn that there is support for progressives.
Condorcet voting also involves ranking all the candidates, but is based on the idea that the winner should be able to beat each opponent in a two way race. Unfortunately, this isn't always achievable, and it is possible for there to be what is called a "Condorcet cycle" like the familiar 'rock paper scissors' game. It's also problematic if there are lot of candidates. Still, it's better than plurality:
Using the same number as above:
Bush beats Gore 90 times
Bush beats Nader 90 times
Gore beats Bush 110 times
Gore beats Nader 150 times
Nader beats Bush 110 times
Nader beats Gore 50 times
So, Gore beats Bush (110 to 90), and Gore beats Nader (150 to 50) and Nader beats Bush (110 to 90), so, Gore wins. But there are times when, e.g. Gore beats Bush, Bush beats Nader and Nader beats Gore.
Instant runoff voting is probably the most commonly used alternative to plurality voting. Again, all candidates are ranked. If one candidate gets a majorithy of first place votes, then he/she wins. If not, then the votes of the person with the fewest first place votes are re-assigned, based on the second-place choice of those voters. So, if, say, out of 200 voters
BGN : 70 people
BNG : 10 people
GBN: 10 people
GNB: 70 people
NBG: 10 people
NGB: 30 people
So, Bush has 80 first place votes, and Gore also has 80; Nader gets 40. No one has a majority of first place votes, and Nader's votes are reassigned to Bush and Gore, based on who those voters picked second: 10 to Bush and 30 to Gore. Then Gore has 110 total and Bush 90 and Gore wins.
This works very well if there are two major candidates and some minor ones, but can lead to odd results when there are several candidates with reasonable numbers of first place votes.
Then there is my favorite (and the other main contender) range voting. In this, each candidate is rated, rather than ranked. That is, you give each candidate a grade (0 to 10, or 0 to 100, or whatever) then the person with the highest average wins. Computer studies show that this is probably the best scheme. Objections to it (mostly from the IRV people) are more practical than mathematical: Theorists say people won't be able to give ratings. I don't think those objections make much sense. In a way, this is the most familiar scheme. Anyone who's ever been graded (that is, everyone) has had this applied to them. One objection is that people don't have enough information to give sensible ratings to people - but psychological experiments show that rating is often easier than ranking. You can also leave a rating blank, if you like.
Since this is a rating and not a ranking scheme, Arrow's rule does not apply.
Part of what I wrote here is accepted by every theorist - that is, plurality voting is a terrible system. The rest is hotly debated. In particular, debates between IRV people and range voting people get extremely heated (it's almost comical). I've read just this one book, and used my math training and common sense to choose. That leads to my poll question