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

[Adam Tarr]

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