Hi, Eric G wrote: -snip- > Unless I am mistaken, Approval Voting does satisfy IIA and > I find AV to be a reasonable system. :-) > > This nuance is missing on the page > (http://en.wikipedia.org/wiki/Spoiler_effect) as well > when it is stated: > > A voting system which satisfies the independence of irrelevant > alternatives criterion is immune to the spoiler effect, > but Arrow's impossibility theorem shows that complete > satisfaction of this property is incompatible with other > desirable properties of an electoral system. > > Arrow's impossibility theorem only applies to ranked ballot > voting methods and AV is not a ranked ballot method.
I prefer more general wordings of Arrow's theorem that apply to all voting methods. The one in my web pages, for instance. Approval fails a "universal domain" axiom, which requires the social ordering function or social choice function accept from each voter any possible ordering of the alternatives. Some people consider universal domain to be a desirable property. The voters' preferences might not be dichotomous, for instance. But this is not why I expect Approval will be disappointing. (I've given my reasons in the past, and don't feel like repeating them here, sorry.) There's a paragraph about Approval in my discussion of universal domain in my web page about Arrow's theorem. I'll copy and paste it here: "On the other hand, we are not really limited to Arrow's framework, which was designed merely to try to aggregate voters' (sincere) preferences. Although it is reasonable to require the voting method to work for any collection of preferences the voters may have, it does not necessarily follow that no constraints should be placed on the expressions voters may make when voting. For instance, the so-called Approval voting method constrains each voter to partitioning the alternatives into two subsets, which is equivalent to a non-strict ordering that has at most two "indifference classes." It is not a priori obvious that the use of voting methods such as Approval, which constrain the voters from completely expressing their preference orderings, are worse for society, so the universal domain criterion should be considered controversial until other arguments not explored by Arrow are examined (assuming those arguments support the conclusion that it is better not to constrain the voters from expressing orderings). In other words, other criteria for comparing voting methods, in addition to Arrow's criteria, need to be evaluated. (My own conclusion is that there are solid reasons why it is better not to constrain the voters' expressions, but that is beyond the scope of this document.)" --Steve ---- Election-methods mailing list - see http://electorama.com/em for list info
