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Book review: Gaming the Vote
This thorough but highly readable book talks about how the US electoral system is broken at the design level, even if all the tactical problems like voting machines and dirty tricks weren't there. He explores the attempted fixes, points out the drawbacks of each with examples, and proposes a solution which has some mathematical support.
The way the US conducts almost all its elections doesn't capture the will of the people accurately, and can't. The problem is one that people here have talked about: the system just plain can't reflect your preferences unless you actually like one of the two major-party candidates.
If the Republicans and the Democrats put up diphtheria and smallpox as their candidates, then supporters of a third party that runs vaccination face a nasty problem. Ignore the sheep who say things like "You're throwing away your vote", "He doesn't have a chance", and in general don't realize what a vote is. There's a real problem: the odds are that if you vote for vaccination, you would otherwise have voted for diphtheria as the lesser of two evils. In that case your vote for what you really want helps to elect smallpox.
Gaming the Vote gives vivid real life examples of this problem and documents many cases where a major party funded a third-party enemy to draw votes from the other major party.
Then the book talks about the nature, the history, and especially the malfunctions of alternatives such as instant runoff voting, approval voting, Condorcet voting and Borda voting. It covers the (often incandescent) theoretical debates about whether the problems of each are significant in real life, in enough detail to be accurate but while remaining clear to a non-specialist. He explains the theorem that all ranking-based voting systems have paradoxes (the Arrow Impossibility Theorem).
Most of the alternatives, except for approval voting and the system Poundstone saves for the end as the best choice, involve letting the voter rank all the candidates in order of preference. In the example above, if the voter is honest (more about that later), the ranking will be vaccination > diphtheria > smallpox.
Instant runoff voting takes the rankings and checks whether any candidate has a majority of first-place rankings. If not, you repeatedly eliminate candidates based on their getting the fewest first-place rankings, and reallocate their supporters' votes to the supporter's second choices until a winner emerges. This way, there's no disincentive to putting your first choice first, and maybe enough people will realize that so that vaccination will actually win.
Poundstone points out analysis by voting theorist Donald Saari that IRV could have led to a "bad" outcome in the Lousiana election that pitted a crook against a Klansman. Other problems show up in theory. Popular moderates can be eliminated early if they're crowded out of first place by ideologues. An apparent paradox, which Poundstone explains, is that ranking a candidate higher in some configurations can cause that candidate to lose. There's also a practical problem: the "instant" in the name isn't quite accurate because you have to total up all the votes before you can begin the actual selection. The more serious effect is that you're completely dependent on a central counting authority.
Condorcet voting takes the rankings and runs pairwise contests using them. Vaccination prevails in all two-way contests, so it wins.
The drawbacks, which Poundstone illustrates with a real-life Wikipedia vote, include the risk of getting into a rock-paper-scissors cycle with no clear winner.
Borda counting awards points to each candidate based on the candidate's rank position, and adds those up across all ballots. It suffers from the problem that it encourages dishonest ballots. If Ebola joined the race in our example, then someone who saw the polls showing Ebola with no chance might rank Ebola ahead of smallpox. Expressing a "preference" for Ebola hurts smallpox's chances, which is why someone might do it, but then the ballot no longer reflects real preferences and Ebola does better than it should.
Approval voting does away with rankings entirely, and is therefore exempt from the impossibility theorem. Each voter says "OK" or "not OK" of each candidate. If chlorination joins our example race, you could vote yes on both chlorination and vaccination and no on the three diseases. This sounds simple and fair but is the subject of bitter academic controversy. The easiest problem to understand is that it doesn't rank preferences: a candidate just barely tolerable enough to approve for most people can beat a candidate who is the enthusiastic favorite of many.
Poundstone accompanies the theory with vivid biographical sketches of the colorful people who have researched and proposed voting systems. He draws examples from real life whenever possible, including the 1992 Bush/Clinton/Perot election.
So what are we supposed to do? Poundstone closes by advocating "range voting", which captures the information other systems miss by having voters give each candidate a rating from 1 to N. Instead of clicking a checkbox or picking a ranking, you can say how much you approve or disapprove of each candidate. Researcher Warren Smith has run simulated elections pitting voting systems against each other on a scale of "Bayesian regret", a measure of how unhappy the simulated voters are with the simulated results. Range voting consistently comes out best.
Read it. It's a rare combination of entertaining and informative.
Gaming the Vote, William Poundstone, Hill and Wang 2008. ISBN 978-0-8090-4983-9