[EM] Simplified ranking in real elections

[MIKE OSSIPOFF]

>Direct election of local mayors in Flanders (Northern Belgium)
>
>Formerly the mayors were elected by the local councils.
>The direct election of the mayors by the population is now being prepared
>(due 2006).

That's a good opportunity to get a genuinely good voting system
like SSD enacted.

>
>If we think about ballots were the candidates are ranked (SSD, Tideman,
>...), then we may expect some practical problems.
>The theoretical procedure may be too cumbersome, especially for the voter.
>
>The larger cities may have 20 or more candidates, possibly some belonging 
>to
>the same party
>(so far I am not aware of an interdiction of multiple candidates of the 
>same
>party running for the mayor-seat).
>Voters will not or only grudgingly rank 20 candidates.

No problem. Voters should be instructed to rank as many candidates
as they want to, as few as 1, or as many as all of the candidates.

Allowing as many rank positions as people want to use in no way
should make anyone feel forced to rank all of the candidates.
Obviously, a voter should at least rank down to the candidate whom
he considers to be his needed compromise, the best he can get.

But, unless some really improbable offensive strategy is used,
no one has any incentive to vote every pairwise preference that he/she
feels. If you're short of time, then maybe you don't want to rank all
20. Especially if you feel sure that your 3rd choice has a win.

But if you don't have a definite idea of who has a win, or if you
just feel like expressing all of your preferences (Lots of people will),
then vote all of your preferences by ranking all of the candidates.

Sure, in our elections here, I must admit that that I'd leave the
Democrats and Republicans out of my ranking, as a matter of principle
and good taste. Since there's no strategic need to vote a short
ranking, someone could say my truncation is poor strategy. Ok, but
that's how I'd vote. There's a limit to what I'll vote for. The
fact that we're allowed as many rank positions as we want doesn't
prevent me from only ranking a few of the best candidates, if that's
how I feel like voting.

>
>I believe this a simple and reasonable simplification, but I would like to
>hear comments or perhaps hear about simulations or other tests.
>
>The simplification thought of is :
>On the ballot there will only a restricted number of ranks possible 
>(perhaps
>3 ... 5)
>and in most cases less than the number of candidates.

That's perfectly ok, if it's needed because of a shortage of space
on the ballot. But it's _not_ needed to help the voter. The voter
can always vote a short ranking, no matter how many rank positions
he's allowed. Voting for all 20 candidates is for the person who
_wants_ to vote for them all, in order to express all of his preferences,
as many will want to. I'd want to myself, if they're all any good.


>People may rank a candidate only once (of course) or not.
>Not ranked candidates receive the lowest rank (one lower than the lowest
>rank on the ballot).

Yes, that's a correct interpretation of a ballot that leaves a
candidate unranked.

>People may rank several candidates in the same rank (example, think of
>people liking a particular party more than another who would rank in the
>same way all the candidates of a party).

I agree that people should be able to rank several candidates at the
same rank position, for the reason that you said.

>
>The Dodgson or vote-matrix is now incremented as follows :

Dodgson fails all of the defensive strategy criteria, which means
that it does a very poor job with regard to getting rid of the 
lesser-of-2-evils problem and majority rule. It seems to me that someone 
also
said that Dodgson fails the Clone Criterion. I read that Dodgson
fails Monotonicity. I don't know how a non-iterative method could
fail Monotonicity, but that's what someone said.

Dodgson fails the Clone Criterion in the worst way, because it has
the "rich party problem": By adding clones, identical candidates,
a party can increase the total margins by which some of their rivals are
beaten, thereby helpilng their own party against the rival party.

If you want the state-of-the-art best, use SSD. BeatpathWinner would
be just as good (they're identical in a public election), but SSD
has natural & obvious motivation & justification.

>For every pair of candidates, compare their ranks, if they are different,
>the cell of the winner-pair in the vote matrix is increased by 2.
>If the ranks are the same for candidates i and j, both cells (i,j) and 
>(j,i)
>are increased by 1.

In Dodgson, for any 2 candidates A & B, if A beats B 50 to 45,
then we call that a 5-vote margin against B. B's score is determined
by adding up all the margins against him, to get his "overall margin
of defeat". The candidate with lowest overall margin of defeat wins.
I've also seen Dodgson defined so that B's score increment in his
defeat by A is the number of voters who'd have to reverse their AB
preference for B to beat A. It's really essentially the same either
way. But Dodgson isn't what you want to use. A candidate's score is
either the number of individual pairwise votes that would have to
be _ignored_ to make him the CW, or the number of individual pairwise
votes that would have to be _reversed_ to make him the CW. I've seen
it both ways. Either way, it isn't what you want.


Mike Ossipoff

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