[EM] 1-Person-1-Vote has been abandoned.

[Stephane Rouillon]

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?
>
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