[EM] Steph: Extremist shouldn't change outcome?

MIKE OSSIPOFF nkklrp at hotmail.com
Sat Jan 18 23:35:45 PST 2003


Say the voting system is Condorcet with relative margins. Say
there are initially 2 candidates, A & B. 51% prefer B to A, and
so, as would any rank method, rm elects B.

Now we add an extreme candidate, C. The A voters don't consider
C to be a serious rival. They believe, rightly it turns out,
that A will pairwise-beat C.

Here are the sincere rankings now:

49: ABC
20: BAC
31: CBA

Because, as I said, the A voters believe that A will pairwise-beat
C, they don't feel that they need to help B. And so they aren't
inclined to help B become BeatsAll winner. They don't rank B.

49: A
20: BAC
31: CBA

Relative margins of the defeats:

CB: (31-20)/51 = 11/51
BA: 1/100
AC: ((20+49)-31)/100 = 38/100

BA has the lowest relative margin, and so A wins.

What would have happened in Condorcet(wv)?

The defeat's wv:

CB: 31
BA: 51
AC: 69

Condorcet(wv) has met your standard better than Condorcet(rm).

What would happen in Approval?:

B is middle, and the middle voters have no good reason to vote
for other than their favorite.

Depending on which extreme appears more likely to outpoll the other,
the extreme voters on one side need Middle, to avoid their last
choice. The side that expects to be outpolled by the opposite extreme
isn't going to also expect to have a majority. They vote for Middle,
which is B. And B wins.

It would seem  that in this plausible example, your relative margins
is the method that lets the addition of the extreme candidate change
the outcome.

Mike Ossipoff

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