other devious electorate solutions

Steve Eppley SEppley at alumni.caltech.edu
Tue Nov 10 13:23:26 PST 1998

Mike Ossipoff <ntk at netcom.com> wrote:
> Steve & Tom Round suggested the candidate withdrawal option
> as a solution for strategy problems for IRO, but it would work
> with any rank-method, including Votes-Against. With that method
> it would completely eliminate the order-reversal problem. An
> advantage is that since reversal couldn't ever work, it wouldn't
> be tried, and therefore the withdrawal would never need to be
> used, except maybe once or twice at first.

Even with the best (pairwise) methods, the Withdrawal option 
would still be used sometimes even when voters don't 
misrepresent their preferences.  Where there is a sincere 
circular tie, it could be advantageous for one of the 
candidates who loses the circular-tie-breaker to withdraw, if 
that "improves" the outcome from his/her perspective.  

(Hopefully, what the withdrawing candidate will receive in 
exchange, from the new winner, is the policy plank which led a 
majority to rank him/her ahead of the new winner.)

The Withdrawal option also mitigates a "problem" with plain 
Condorcet-EM, that it can violate the Smith criterion (and it 
can even elect a "Condorcet Loser", which is an alternative 
which loses pairwise to each other alternative).  For 
instance, suppose there's a 4-candidate election where A, B, 
and C are circularly-tied clones and D is a Condorcet Loser:

   20: ABCD
   20: BCAD
   20: CABD
   13: DABC
   13: DBCA
   13: DCAB

          The pairwise tally table:
                    x>A   x>B   x>C   x>D
      A vs B?       33    66L
      A vs C?       66L         33
      A vs D?       39                60L
      B vs C?             33    66L
      B vs D?             39          60L
      C vs D?                   39    60L
   D loses all three of its pairings, 39<60.
   But A, B, and C all have max "votes against" of 66.
   Since 60<66, if no one withdraws then plain Condorcet-EM
   will elect D.

   If any one of A, B, or C withdraws, D will be defeated.
   Since all three appear to have an incentive to defeat D,
   we can expect that one of them will withdraw.

A plausible measure of a voting method's "goodness" may be the 
frequency of withdrawals.  The fewer withdrawals, the better 
the method.  (We should probably also count candidates who are 
eliminated in primaries, or who announce but withdraw before 
the election, as "withdrawn" candidates, for comparison's 

For simplicity's sake, where the withdrawal option is allowed 
I'd also wholeheartedly support methods which are simpler than 
pairwise methods, even though simpler methods will make 
withdrawals far more likely.  For instance, the simplest 
preference voting method is "plurality wins"; combined with 
just-in-time withdrawals this method would be easy to 
understand, and reasonably good assuming we can rely on 
candidates to not needlessly be spoilers.  (I'd also 
wholeheartedly support IRO if candidates may withdraw after 
the voting before the tally is finalized, but it's not clear 
that IRO's iterative eliminations are truly easier to 
understand than pairwise methods.  There's only an unproven 
assertion of this by IRO advocates, with no evidence 
supporting it.)  Eventually, as voters grasp the principles, 
they will switch to more complex methods where withdrawals are 
needed less.

I heard that Santa Clara County (in California) elected to 
adopt IRO in county/local elections.  It would be interesting 
to ask whether they will allow candidates to withdraw after 
the voting, and also whether they will publish the ballots on 
the internet before the tally is finalized so candidates can 
calculate whether they should withdraw.  Probably neither of 
these has occurred to the powers-that-be in Santa Clara.  I 
haven't read the election laws there; perhaps it's already 
possible for candidates to withdraw just in time.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)

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