William Poundstone: Gaming the Vote, Hill & Wang 2008.
Because I am mentioned in it quite a lot, it would be inappropriate for me to offer a full review of Poundstone's book (but see the New York Times's.) But I see that Nobelist Kenneth Arrow is both (a) mentioned in it a lot, and (b) wrote praise for the book on the book cover. So I feel I can say something. So here are several statements.
1. As Martin Gardner points out in his quote on the book cover, Poundstone "defends range voting as the best system yet invented... there is no better introduction to the inescapable paradoxes and flaws of all voting systems than this eye-opening timely volume." I agree.
2. Overall I think Poundstone's is definitely the best voting methods book for the lay reader. It's the most fun to read (not even a contest there). Also, in some ways it's the best-researched book in the sense that only Poundstone – and no other human being – has interviewed all the key players like me, Arrow, Brams, Weber, Saari, hotornot.com, etc, and tracked down their original thinking.
3. This is a tremendously important subject – it is not often-enough realized how important.
4. For the professional reader, Poundstone's book is inadequate, but there presently is no adequate book and it's a good start. For example, no voting methods book besides Poundstone's exists that covers range voting or Bayesian Regret or Myerson's "equilibrium" in any serious way. No voting methods book out there at all has a good discussion of 2-party domination (and see below for me attempting to contribute toward that).
5. Poundstone also dug up some stuff I, an alleged top expert, did not know, and I bet that is true for every reader not just me. (For example, some of the paradoxes suffered by Instant Runoff Voting were first pointed out by... Lewis Carroll! I found that out after following a tip from Poundstone.) He digs hard, doesn't have any sacred cows, almost-entirely avoids taking anything on trust, and makes everybody earn it. I like that.
Now I report on an important thing Poundstone did not adequately explain or comprehend in his book: the nursery effect and 2-party domination.
Two-party domination happens in some voting systems and not others. That's very important. As Duverger noted, plurality elections lead to 2-party domination setting in. In the USA it is now massive. But the French system of (non-instant) runoff elections (2 rounds) does not seem to lead to 2-party domination. The IRV system does seem to lead to 2-party domination. (Subtle difference there. Evidence and discussion of possible reasons.)
If you want evidence from Australia, Malta, Ireland, and Fiji, see e.g.
The fact IRV leads to 2-party domination is very important because if there is 2-party domination, then the extra choice voters might hope to take advantage of with a better voting system, is illusory.
That in my view is one of the most major, if not the most major, criticism of IRV.
Non-monotonicity, poor Bayesian regret, favorite-betrayal, all happen with IRV and are not so good, but as Poundstone & Richie say, we could live with them. ( Analysis of non-monotonicity commonness.)
But I really have trouble living with being stuck with 2-party domination forever, and hence minimal voter choice forever. IRV will lock that in stone. (Especially in the USA, which since it clearly has more 2-party-genic factors than Australia, Ireland, and Fiji – e.g. directly-elected president, non-parliamentary, no PR component of the government, already-established 2-party domination – for sure with IRV would stay 2-party dominated with IRV.)
Now you may ask: why does IRV lead to 2-party domination?
You immediately can see why plurality does – voting third party is a wasted vote, so people don't do it, so third parties die out over time. That justifies voters' original decisions to betray third party favorites all the more: so we get a self-reinforcing vicious cycle.
With IRV, it is more subtle.
First, the IRV spoiler effect (see also this, etc) causes it to be wise to betray your third-party favorite (i.e. not vote him top) provided his chances of winning are small compared to the chance an IRV spoiler scenario will happen. The numbers from both history and theory say that numerical criterion is true. So the decision to betray third party favorites is rationally justified. So they get betrayed. So third parties lose. So they die out over time. Self-reinforcing vicious cycle.
Second, maybe voters were not smart enough to know that. Fine. The dumb voters will just rank the Dem & Repub artificially top & bottom to "maximize impact." Maybe that doesn't really make sense. But they do it anyway because we just postulated they are dumb, plus as I explained with the IRV spoiler effect, it actually isn't dumb. Fine. If enough voters do this, then a third party candidate can never win. Game over.
Third, the vast majority of Australians clearly do vote "strategically" in exactly this kind of manner. So it does happen and it does dominate the picture.
This all was not discussed in Poundstone's book, really, and the Nursery Effect discussion ended up a bit left out in the cold, not developing its full potential, and failing to make this major point about why IRV is bad news and why, in contrast, there is strong evidence Range Voting will be highly beneficial to third parties.
And note, this goes beyond any Bayesian Regret study. That study was about "direct effects." Two-party domination setting in is an Indirect Effect (happens only over a sequence of many elections, not just one). It thus was invisible to the Bayesian Regret study. When you try also to reckon such indirect effects, IRV looks worse than the Bayesian Regret study alone would indicate, while Range Voting looks better. Indirect effects vis-a-vis other voting systems are examined in my paper #76 here.
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