The "problem" with circularity (was Re: Reply to Blake Cretney)

[Hugh R. Tobin]

Steve Eppley wrote:
>
>Perhaps Donald didn't understand the "truncation resistance" property 
>of the Condorcet and Smith//Condorcet methods which led the 1996 poll 
>in the EM maillist.  Some other variations, such as measuring the 
>size of a candidate's pairloss by taking the margin of difference in 
>that pairing (instead of by counting the voters who ranked the 
>pairwinner ahead of the pairloser), would be more susceptible to 
>truncation.  Truncation might be done strategically given methods 
>which aren't truncation-resistant, or innocently because a voter 
>wanted to finish voting early.  Truncation resistance means that the 
>voter does not have a strategic incentive to rank only one, since 
>that strategy won't help the voter.  And it means that innocent 
>truncation won't affect outcomes either (unless a lot of voters 
>foolishly truncate the compromise candidate who needed their votes).
>
I feel I must mention for the benefit of recent subscribers, though it
covers old ground:
The TR quality of S//C [EM] is better described as a penalty for sincerely
voting only true preferences, or an incentive to random voting towards the
bottom of one's ballot when one has no preference between pairs, or indeed
no knowledge of them (a very common situation in local nonpartisan elections
and even statewide races for offices that do not attract major media
campaigns, such as judgeships).  It is established that in the general case
(in which the voter lacks the ability to predict the more likely direction
of a circular tie), a rational voter will use the random voting strategy in
S//C[EM], but would have no incentive to do so in S//C [margins].

I still find Steve's argument that [EM] somehow leads to better results than
margins when there is "innocent" truncation baffling, because (a) no system
can implement reliably the unexpressed preferences of the voters; (b)
"truncation" means failing to express a preference that one actually holds,
even though one has taken the trouble to cast a ballot; and (c) the only
logical inference we can make when a voter truncates without a strategic
motivation is that he or she has no further preferences. 

I have earlier argued, without contradiction, than in S//C [margins]
strategic truncation is only a weaker form of order-reversal, with no
independent significance.  In particular, there was no answer to my
question, what set of expectations regarding the probability distributions
of votes of others could lead a voter to truncate, but not to reverse order.

The real advantage of [EM] tiebreaker over margins is that it permits a
voter with a milder preference at the top of his or her ballot to minimize
the chance of a despised candidate prevailing by suppressing that milder
preference.  As Markus Schulze has pointed out, in [EM] one would have an
incentive to reverse truncation that is not present in margins.  If this
incentive is regarded as a problem, then [margins] is clearly superior to
[EM], in that is will produce more sincere rankings.  But if one believes
that a voter should be able to choose to vote as strongly as possible
against a least favored alternative, at the cost of milder preferences, then
one should consider a hybrid tiebreaker for S//C such as I proposed in my
first posting on this list: count equal rankings as zero when there is
another candidate in the Smith set whom the voter ranked below the equally
ranked candidates; count them as one-half otherwise.

In this way equal rankings are more likely to count as the voter with
preference profile A>B=C would wish: to help A defeat each of B and C in
case of a circular tie; without (as in margins) counting A=B>C as the voter
would not wish, as one-half vote against each for purposes of a tiebreak
comparison with C's loss to A or B.

However one may regard such a hybrid system, one should not be misled into
thinking  that it is [margins] that deters voting of sincere preferences.
In fact, it is EM that deters  expression both of sincere preferences (at
the top of one's ballot) and sincere indifference (at the bottom of one'e
ballot).  In my opinion, the deterrence of the former has a compensating
benefit to the voter; the deterrence of the second has no redeeming virtues
-- because, again, deterrence of strategic truncation has no significance
when order-reversal is available, and any arguments about the effects of
"innocent" truncation rest on unjustified assumptions about actual
preferences that the voter is hypothetically concealing.

If advocates of "beat-path" methods believe there is any merit in the
arguments for a hybrid tiebreaker above, I would be interested in analysis
of how such a concept might apply in such systems.

-- Hugh Tobin