First Debate on DEMOREP1's 2-1-2 Example

[Hugh Tobin]

donald at mich.com wrote:
> 
> Dear Methods list,
> 
> DEMOREP1 wrote:
> >Example-
> >2 AM
> >1 MB
> >2 BM
> >
> >With IRO, M is dropped so that B wins, 3 to 2.
> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
> Donald writes,
> Dear DEMOREP1, I am willing to accept your Instant Run-off example for
> debate but I have some conditions.
> 
> Condition One: These five voters are experienced in three election methods
> - Plurality - Instant Run-off - Condorcet.
> 
> Condition Two: Before the election the voters are told which method is
> going to be used to crunch the results - and only that method can be used
> on the returns of that election.
> 
> Condition Three: There is to be three elections on one ballot - Plurality -
> Instant Run-off - Condorcet - as follows:
> 
>     Plurality       |        Instant Run-off     |        Condorcet
>    vote for one     |           1   2   3        |          1   2   3
>        A []         |        A []  []  []        |       A []  []  []
>        B []         |        B []  []  []        |       B []  []  []
>        M []         |        M []  []  []        |       M []  []  []
> 
> I say the results of these three elections will be as follows:
> 
>     Plurality       |        Instant Run-off     |        Condorcet
>        2 A          |            2 AM            |           2 A
>        2 B          |            2 BM            |           2 B
>        1 M          |            1 MB            |           1 M
> 
> The Instant Run-off results are the same as your example.
> The results of the Condorcet election will be the same as the Plurality
> election. The reason for this is because EXPERIENCED voters in a Condorcet
> election will not make a second selection - because they know that the
> second selections will be used to help some candidate other than the
> candidate of their first choice.
> 
> [snip]

You are right that we should expect voters to take into account how the
system will use their preferences, but wrong in assuming truncation is
generally optimal strategy.  In Condorcet a voter does not necessarily
maximize his favorite's chances by truncating, and generally does not
maximize the expected value of the electoral outcome to him by doing
so.  Indeed, one may cause one's favorite to lose by failing to pick a
second choice, especially in the Condorcet version that counts equal
rankings as zero for each, rather than 1/2, as one example I posted
months ago illustrated.  But the main problem with truncating is that
one's least favorite may win over an intermediate choice who might have
prevailed had one cast a sincerely ranked ballot.

In the 5-voter example, why should the M voter truncate and get a coin
toss between A and B (as in your results), when M prefers B to A? 
Surely he will vote MB. In that case why should the A voters truncate,
allowing B to win, when by hypothesis, the A voters prefer M?  Surely
they will vote AM.  The B voters could cause a circular tie by
truncating, but then M is least-beaten (2-1, by A), and wins.  If the B
voters split their second choices (BA, BM), then there is a 3-way tie in
the Condorcet tiebreaker (it is not clear that B voters would want this,
with a risk that A wins the drawing of lots). I do not regard this
result as exposing a defect in Condorcet, because with such a small
number of voters a tie is not surprising, whether or not strategy is
employed.  The more difficult problem for Condorcet arises when B has
more than 40% first place support in an otherwise similar scenario (20%
middle), and B supporters thus could use order-reversal to create a
circular tie that B could win. 

-- Hugh Tobin

> Donald,