On Fri, Oct 28, 2011 at 2:43 AM, Jameson Quinn <[email protected]>wrote:
> What makes a single-winner election method good? The primary consideration > is that it gives good results. The clearest way to measure the quality of > results is simulated voter utility, otherwise known as Bayesian Regret (BR). > > This is not the only consideration. But for this message, we'll discount > the others, including: > > - Simplicity/voter comprehension of the system itself > - Ballot simplicity > - Strategic simplicity > - Perceived fairness > - Candidate/campaign strategy incentives > > > Calculating BR for honest voters is relatively simple, and it's clear that > Range voting is best. But how do you deal with strategy? Figuring out what > strategies are sensible is the relatively easy part; whether it's > first-order rational strategies (as James Green-Armytage has worked > out<http://www.econ.ucsb.edu/~armytage/svn2010.pdf>) > or n-order strategies under uncertainty (as Kevin Venzke does) or even just > simple rules of thumb justified by some handwaving (as in Warren Smith's > original BR work over 10 years ago), we know how to get this far. But once > you've done that, you still have to make some assumptions about how many > voters will use strategy. There are several ways to go about this. In order > of increasing realism, these are: > > 1. Assume that voters are inherently strategic or honest and do not > respond to strategic incentives. Thus, the number of voters using strategy > will be the same across different systems. Warren Smith's original BR work > with IEVS seems to have shown that Range is still robustly best under these > conditions. Although I am not 100% convinced that his definition of > strategy > was good enough, the results are probably robust enough that they'd hold up > under different definitions. > 2. Avoid the question, and just look at strategic worst cases. I count > this as more realistic than the above, even though it's just a special case > of 100% strategy, because it doesn't give unrealistically-precise numbers. > But of course, if I say that method X has a BR score somewhere between Y > and > Z, and method A has a BR between B and C, if Y<B<X<C I cannot conclude that > X is better than A. So you lose the ability to answer the important > question, "which method is better?" > 3. Try to use some rational or cognitive model of voters to figure out > how much strategy real people will use under each method. This is hard work > and involves a lot of assumptions, but it's probably the best we can do > today. > 4. Try to get real data about how people would behave in high-stakes > elections. This is extremely hard, especially because low-stakes polls may > not be a valid proxy for high-stakes elections. > > As you might have guessed, I'm arguing here for method 3. Kevin Venzke has > done work in this direction, but his assumptions --- that voters will look > for first-order strategies in an environment of highly volatile polling data > --- while very useful for making a computable model, are still obviously > unrealistic. > > What kind of voter strategy model would be better? That is, what factors > probably affect a voters' decision about whether to be strategic? I can > think of several. I'll give them in order from easiest explanation to > hardest; the order below has nothing to do with the relative importance. > > First, there's the cognitive difficulty of strategizing versus voting > honestly. In a system like SODA, an honest bullet vote is much simpler than > a strategic explicit truncation, so we can expect that this factor would > lead to less strategy. In a ranked system, it is arguably easier to > strategically exaggerate the perceived frontrunners (Warren's "naive > exaggeration strategy" or NES) than to honestly rank all the candidates, so > we might expect this factor to increase strategizing. Note that the > cognitive burden for strategy is reduced if defensive and offensive > strategies are the same. For instance, under Range, exaggeration is always a > good idea, whether it's offensively or defensively. > > (Note: This overall cognitive factor is probably most important for "lazy > voters", and such "lazy voters" are also probably open to strategic and/or > honest advice from peers, so the cognitive factor is perhaps not too > important overall.) > > Second, there's offensive strategy. The more likely it is that strategy > will be advantageous against honest opponents, and the more advantageous it > is likely to be, the more strategy people will use. The first question has > been addressed by the Green-Armytage > paper<http://www.econ.ucsb.edu/~armytage/svn2010.pdf>; > it appears that IRV is relatively strategy-resistant, Condorcet is middling, > and Range and Approval are likely to be subject to strategy. But remember, > the whole point of this discussion is that strategy is not so much a problem > in itself, as an input to the model for determining BR. If Approval gives > better results under 100% strategy than IRV does with 0%, then Approval is > still a better system. > > Third, there's defensive strategy. Basically, this means looking at the > probability that the result will be subject to strategy from some other > group, and seeing if you can defend against that. > > Fourth, there's peer pressure. If you feel that everyone else is > strategizing, you are more likely to do so yourself. This raises the > possibility of positive feedback and multiple equilibria. > > It is crucially important to understand that defensive strategy is not like > offensive strategy in terms of peer pressure. If you think that your allies > are unlikely to back you up on your offensive strategy, you may decide it's > pointless to attempt it. But some people will use defensive strategy merely > as insurance. Thus, there is more likely to be a "floor" for defensive > strategy, a certain number of people who use it even if nobody else is. But > it is also true that the more people use strategy, the more people will > worry about defensive strategy. Thus, a method where defensive strategies > are likely to be possible is more likely to be driven to a high-strategy > equilibrium, than one where only offensive strategies are an issue. > > So, what does all this mean for BR calculations? Well, first, we should try > to characterize the different systems in terms of the first three factors > above. For the cognitive factor, can we develop some objective measure of > how cognitively difficult it is to work out a good strategy under different > systems? For the offensive strategy factor, we can thank Green-Armytage for > making a good first step in giving the *probability* of strategic > vulnerability, but we should follow up by working out the *amount* of > strategic advantage a voter could expect. For the defensive strategy factor, > Kevin Venzke's work gives some interesting clues, but more work is needed to > isolate defensive factors. > > But even once we have all that nailed down, we need a voter model to turn > it into a BR measure for each system. Of course, any such model will be open > to accusations of bias, as it will include varying amounts of strategy under > different voting methods. Range voting advocates in particular might be > motivated to assume that strategy percentage will be the same under > different systems. But it's important to undersand that no assumption here > is unbiased; without real-world data, assuming equal strategy is at least as > biased as a model which accounts for the factors above. > > So in the end, I'm inclined to bite the bullet, and make arbitrary > assumptions for now. I'd guess that a method where the factors above favor > strategy --- for instance, Range voting, where all three of the > a-priori-quantifiable factors favor strategy --- would lead to a high degree > of strategy, something around 75%. Meanwhile, a method where the factors > favor honesty --- such as, I'd argue, SODA --- might have a low amount of > strategy, something under 25%. Something like Condorcet or Majority Judgment > has the factors somewhere in the middle, but it would be harder to guess > what that would mean in practice; I'd guess that peer pressure feedback > would mean that either <25% or ~75% would be more likely than an unstable > middle value like 50%. > > Again, the end "quality" number is not strategy percentage, but the > resulting BR. So even if range does lead to more strategy than any other > system, it could still end up being the best system. I'd like to see real > numbers on this. Any assumptions will be biased, but that doesn't make the > numbers useless. > > Jameson > I agree with this analysis, and would also like to see real numbers on this. ~ Andy
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