New sw method: "extreme scale"
Steve Eppley
seppley at alumni.caltech.edu
Sun Feb 23 09:53:38 PST 1997
Here's a new single-winner method which appears to rigorously satisfy
one of Mike Ossipoff's "No Lesser of Evils" criteria:
There must be some way for a majority to rank their favorite ahead
of their lesser evil without risk of electing their greater evil.
The interesting feature about this new method is that it's not a
ranked ballot method. It's a rating method.
Define E to be the number of eligible voters.
Define C to be the number of candidates.
Define S to be 2EC rounded up to the next power of 10. This may
be a huge number. For example, with C = 3 candidates and E = 100
voters, 2EC is 600, so S = 1000.
1. Each voter rates each candidate on a scale ranging from 0 to S.
2. The score of each candidate is the sum of the ratings assigned it
by the voters, normalized by dividing by S. The winner is the
candidate with the highest score.
Except for the huge scale, this simple method should be very familiar.
The advantage of the huge scale is that even though smart voters will
vote near the extremes (0 or S) for most or all candidates due to
strategy concerns, it's possible for the voter to rate a true
favorite higher than a lesser evil without fear of electing the
greater evil, if the voter knows s/he is part of a smart majority
which prefer the lesser evil more than the greater evil.
Example: 3 candidates A, B, and C. 99 voters. S = 1000
49: A > B
50: B > A
Suppose some of the 50 also prefer C more than B.
They can vote:
A = 0
B = 999
C = 1000
As long as all 50 of the majority rate B at least 999, B's score will
be at least 49.950. If they also rate A=0, then even if all 49 A
supporters vote A = 1000, A's score will be at most 49.000.
The basic voting strategy would presumably be to rate best
"compromise" candidate(s) you think you'll be able to elect
extremely high, but less than those you prefer more. For instance,
if your preference order is ABCDE and you think you're part of a
majority which prefers C more than D & E, but that there isn't a
majority which prefers A or B more than C, than you'd vote:
A= S
B= S-1
C= S-2
D= 1
E= 0
A conjecture: If the pre-election poll data includes the preference
order info available from this method or from a ranked polling
method, the voters will often be able to determine how far they'll
have to compromise.
But even if the voters compromise unnecessarily, or don't compromise
far enough, so the winner is less than the "best" possible, at least
the preference order information needn't be misrepresented.
Arguably, the two most important standards for single-winner
election methods are "No Spoiler Dilemma" and "Minimize Incentives
to Misrepresent Preference Orders", in order to avoid submerging
majority opinions on important issues. Since this "extreme scale"
method is fairly simple to understand, and since it satisfies one of
the lesser evil criteria, it may be worth examining its incentives
regarding potential candidates and voter behavior.
---Steve (Steve Eppley seppley at alumni.caltech.edu)
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