[EM] Are tied rankings valid in IRV?
Rob Lanphier
robla at robla.net
Sun Apr 20 14:27:19 PDT 2003
Alex Small wrote:
>Let's look at a scenario where IRV encourages insincere rankings, and see
>if generalized IRV would encourage equal rankings rather than reversing
>the order of 2 candidates.
>
>Say that your preference is A>B>C, and no candidate has first place votes
>from a majority of the voters but C has the lead in first place votes.
>Say that B beats C pairwise, and C beats A pairwise.
>
>You don't want B to be eliminated, so you definitely rank him first.
>However, you do want A to be eliminated. Although there will be cases
>where ranking A and B equal will suffice to push B ahead of A, there will
>still be cases where you also want to rank A second, to ensure that A is
>eliminated rather than B.
>
>
>A second case: Your preference is still A>B>C. A has enough first place
>votes to not be eliminated, but B and C are in a close race. A beats C
>pairwise but B beats A pairwise. You want B to be eliminated, so you
>don't rank him equal to A, but you want C to advance, so you rank him
>equal to A. There's no disincentive to rank A in first place, so your
>ranking should be A=C>B.
>
I'd like to spell this scenario out to clarify how it would work.
Let's say that the sincere rankings would be
40:A>B>C
16:B>A>C
15:B>C>A
29:C>B>A
In this particular race, the Condorcet winner would be B, and the IRV
winner would also be B (just barely, thanks to a first round elimination
of C). So, some A voters would be motivated to engage in order reversal
under standard IRV, but that would be a risky strategy. Under tied-pref
IRV, a bunch of A>B>C voters could have tied rankings in first place:
37:A>B>C
3:A=C>B
16:B>A>C
15:B>C>A
29:C>B>A
This would give C the edge over B in the first round (A: 40, B: 31,
C:32). The final election would be (A: 56, C:47). Not too many folks
could do this, though, without risking an election of C.
Also not that other voters could engage in a defensive (even offensive)
strategy similar to Approval. The most obvious example would be the
folks who prefer C>B>A:
37:A>B>C
3:A=C>B
16:B>A>C
15:B>C>A
3:C=B>A
26:C>B>A
Now the first round is (A: 40, B:34, C: 32). C is eliminated. In fact,
the correct voting strategy is exactly the same as Approval (vote for
all candidates preferred to the leading candidate, and the leading
candidate if preferred to the second place option). If the (B and C)>A
voters use Approval strategy, they are pretty unassailable from
tied-pref attacks from A:
37:A>B>C
3:A=C>B
16:B>A>C
15:B=C>A
29:C=B>A
Here we see that the result is (A: 56, B: 60, C: 47). C is eliminated
in the first round, and B beats A. There's nothing that A voters can do
to affect this, since the only thing that greater A=C>B votes does is
pump up C to the point that it eliminates A from the race.
So, I'm becoming convinced that tied-pref IRV behaves like Approval.
However, I'm also becoming convinced that IRV advocates would never go
for it, because it looks *too much* like Approval.
This points out something that is superior about Condorcet voting. It
pretty gracefully handles tied rankings, in a way that doesn't
profoundly impact strategy. This seems like a good talking point to
those that would argue in favor of IRV over Condorcet.
Rob
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