[EM] 1-Person-1-Vote has been abandoned.
Adam Tarr
atarr at purdue.edu
Wed Jan 15 08:20:33 PST 2003
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?
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