Mike Ossipoff wrote previously: >Judge them by criteria. Approval meets FBC & WDSC. IRV meets Mutual >Majority (MMC). But, as I discuss below, every MMC example is an IRV >failure example in wihch IRV fails FBC & WDSC. One must choose which is >more important.
Since before the dawn of time, Mike Ossipoff has been arguing that approval is superior to IRV because approval satisfies these criteria: FBC and WDSC. I agree that it does satisfy the criteria, but I don't think that this fact is impressive enough to settle the issue. First let me quote the definitions of the terms, from electionmethods.org Favorite betrayal criterion / FBC: "For any voter who has a unique favorite, there should be no possible set of votes cast by the other voters such that the voter can optimize the outcome (from his own perspective) only by voting someone over his favorite." Weak defensive strategy criterion / WDSC: "If a majority prefers one particular candidate to another, then they should have a way of voting that will ensure that the other cannot win, without any member of that majority reversing a preference for one candidate over another." The key to both of these criteria is incentive to *reverse* the order of your preferences. A broader criterion which envelops these would be the strategic reversal criterion (SRC), which I'm making up now if it doesn't exist already: "For any set of voters that share a sincere preference ranking of the candidates, there should be no possible set of votes cast by the other voters such that this set would achieve a more-preferable result by ranking / rating a candidate who they prefer less above a candidate who they prefer more." Condorcet, IRV, and a great deal of other ranked ballot methods fail this criterion. Actually, so many good methods fail it that it is rather useless as a criterion in itself... what is more useful is to talk about the *degree* of strategic reversal incentive (SRI) in a given method. But, wait, approval passes SRC. Wow!!! That seems really cool, until you stop to put it into perspective. The strategic reversal criterion should not be considered without considering its twin, the strategic compression criterion (SCC). The strategic compression criterion could be worded as follows: "For any set of voters that share a sincere preference ranking of the candidates, there should be no possible set of votes cast by the other voters such that this set would achieve a more-preferable result by ranking / rating a candidate who they prefer less equal to a candidate who they prefer more." This is identical to the SRC definition except that I have substituted the words "above a candidate they prefer more" with "equal to a candidate they prefer more." Once again, so many methods fail SRC that it isn't really very useful in itself. What is useful is trying to understand the *degree* of compression incentive in a method (SCI). What I'm trying to say is that there are two types of strategic manipulation, one is REVERSAL and one is COMPRESSION, or insincere equal-ranking. If a method passes SRC, you shouldn't get too excited about its strategic properties until you see how it does with SCC. Cardinal ratings is the best example of this. It passes SRC with flying colors. But how does it do with regard to SCI? It does horribly with SCI. While other methods that allow equal ranking (such as Condorcet and equal rankings IRV) will in some cases give incentive for strategic compression, cardinal ratings will *almost always* give incentives for compression. And, typically, CR will give you incentive to compress *more* of your preferences than Condorcet will. Thus, you can meaningfully say that the compression incentive is much much more frequent and severe in cardinal ratings than it is in those other methods. My main point is this: BOTH ORDER-REVERSAL AND COMPRESSION ARE DISTORTIONS OF VOTER PREFERENCE! That is, incentives for order-reversal can be a real problem. They are a problem for IRV, for Condorcet, and so on. There's no getting around that fact. They distort voter preferences and can lead to different outcomes from the sincere preferences, while at the same time making it impossible to know what the sincere preferences were. However, incentives for compression are ALSO A VERY REAL PROBLEM, for the same reasons. There is a lot of really important information that you will lose when voters engage in compression strategy. All else being equal, is reversal more severe than compression? Yes, it is. If one method gives compression incentives about as often as another method gives reversal incentives, I'd probably take the first method, all else being equal. However, what if it's a choice between one method that only has a moderate amount of reversal incentive versus a method that has a very severe amount of compression incentive? That is, the second method compels compression more often than the first method compels reversal, or the second method typically compels many more preferences to be compressed than the first method compels preferences to be reversed. Which brings us to approval voting. Not only does it always give incentive to compress their preferences, it always *FORCES* voters to compress their preferences! So you are not only encouraging distortion of preference, you are mandating it. Mike Ossipoff wrote: >And before someone argues that WDSC & FBC aren't to be found in journal >articles, I suggest that criteria be judged on their own merits. >Millions >of voters are cowed by the lesser-of-2-evils problem, so that they bury >their favorite because of it. It matters what a majority has to do in >order >to make a greater-evil lose. It matters to those millions who are going >to >bury their favorite in November for that purpose. I agree with you here. The lesser of two evil problem is a serious one indeed. A method that has incentive for strategic reversal is problematic, and IRV has reversal incentive in a pretty bad way. In particular, it often compels voters to reverse as part of a "compromising" strategy. I don't mean to belittle or ignore this point. My point is that, while reversal is a serious problem, compression is a serious problem as well. And it is possible for one method's compression incentive (or mandate) to be more problematic than another method's reversal incentive. sincerely, James P.S. I don't really want approval *or* straight IRV in public elections, although I will admit that they are both substantially better than plurality. But at this point I think that I would prefer equal-rankings-allowed IRV (with whole votes) over approval. ---- Election-methods mailing list - see http://electorama.com/em for list info