Adam -- as a matter of fact "fractional voting" methods allow a voter to use its full ballot without having any impact on the result. I could vote .25 for the four candidates I am presented with and clearly have no influence over the result. So I think it fits when the "reciprocal fairness" criteria rejects "fractional voting" methods. But maybe these methods do respect your interpretation of 1p1v...
Steph. Adam Tarr wrote : > Steph wrote: > > >Suppose two sets, S1 the set of voters and S2 the set of candidates. > >Suppose an electoral method that produces scores for each candidate. > >If you can split S1 in |S2| subsets each of a cardinality equal to the score > >obtained > >by the corresponding candidate, you can link these two sets using a bijective > >mapping. Each voter contributes to one and only one candidate. > >If an electoral method produces scores that verify this property, > >it respects reciprocal fairness. > > While I think this is a valid definition, I don't think it represents > EITHER the "spirit" of one person, one vote, OR the "equal voter power" > idea that you are striving for. > > The most simple counter example of this I can think of would be a > "fractional voting" system. By this, I mean an election method where each > voter gets one vote, which they may split among as many candidates as they > like. So, for example, I could give half my vote to one candidate, and a > quarter of my vote to two other candidates. > > Clearly, such a method would violate your "reciprocal fairness" criterion, > and yet it seems obvious that each voter has the same total voting power - > namely, one vote. So I don't think your reciprocal fairness criterion > really represents the idea of one person, one vote in a meaningful way. > > As I've said before, it's very hard to make a meaningful and applicable > criterion from 1p1v, because you're really talking about the machinery of > the method rather than the results. Your stab at a reciprocal fairness > criterion sort of reveals this -- while it's clear that plurality passes > and approval and Borda fail, it's unclear (to me, anyway) how you would > apply this criteria to IRV or to Condorcet. (If IRV can be construed to > pass, then so should approval - since it has been shown that approval can > be implemented as a plurality runoff. Again, your criterion seems very > dependent on the machinery of the method as oppose to the result.) And > I've already shown that the criterion gives unintuitive results for other > methods. > > Alex already noted that the original idea behind 1p1v is captured by > Markus's anonymity criterion, which is passed by any non-probabilistic > method. Just to re-state that criterion, it's just that, "swapping voters > should not change the result of the election." So every voter, upon > stepping into the voting booth, has the same opportunity to make an impact > on the election. > > Now, I agree that 1p1v can be extended beyond this. But I can't formally > state my impression of the "spirit of 1p1v" in a meaningful way. I'll take > a stab at a heuristic definition. I stress that this is NOT a formal > criterion and I would not expect to be able to consistently apply this to > new methods. Anyway, it goes like this: > > **There is a maximum impact (called "one vote") that a single voter can > have on the final result of an election. If a voter knows the votes of > every other voter, the voter can always vote in such a way as to have this > maximum impact.** > > Again, this is not a formal criterion in any sense. But this is what I > think when I hear one person, one vote. So, let's look at some common > election methods, and list the "maximum impact" strategy: > > plurality: vote for either of the two front-runners. > > approval: vote for either, but not both, of the two front-runners. > > cardinal rankings: give one front-runner a maximum rating, and one a > minimum rating. > > IRV: include at least one of the two front-runners in your rankings. > > Borda: Fully rank the candidates. Rank one of the two front-runners in > last place on your rankings, and one in first place. (Borda violates 1p1v > if not all precincts have the same candidate lists, or if some precincts > allow write-ins while others do not. Intuitively, I feel Borda DOES > violate 1p1v, but formally I can't show it. Again, results versus machinery). > > Condorcet: Fully rank the candidates. (I really am not sure how you can > apply the concept of 1p1v to Condorcet, given the possibility of circular > ties in the preferences. In the end, I think the only way to look at > Condorcet in the context of 1p1v is to view each pairwise election > individually. With this in mind, fully ranking allows the voter to cast a > vote in every pairwise contest.) > > So, by my reckoning, every commonly discussed single-winner election method > passes 1p1v, although Borda sort of teeters on the edge, and Condorcet > doesn't really fit rules of 1p1v at all. Well, that's the best I can do, > and I don't think it's particularly meaningful or applicable. Can anyone > do better? > > ---- > For more information about this list (subscribe, unsubscribe, FAQ, etc), > please see http://www.eskimo.com/~robla/em ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
