Goldman & Pereira's "IRV worse than plurality" examples; and how frequent this is

[Warren D Smith]

Brian Goldman's "IRV worse than plurality"
example now enshrined on a CRV webpage:

http://rangevoting.org/IRVworsePlur.html

there also already had been a 4-candidate example by Pereira:

http://rangevoting.org/IRVpereira.html

Jameson Quinn (I think it was) earlier in the
"Thoughts on Maine IRV" thread, erroneously claimed
IRV could not be worse than plurality with same ballot set. It is nice
to have pages such as these to refute such misconceptions.

Re the question about how frequent this is, the first problem is that
what is the DEFINITION of "IRV performs worse than plurality"
in any particular election? If all the voters had utilities for everything, ok
we could define that, but that'd be messy. But without that, there's really
no answer. But...

See puzzle 34B here
http://www.rangevoting.org/PuzzlePage.html
to realize that it is common for IRV to fail to elect Condorcet winners.
Indeed that should happen asymptotically 100% of the time in a limit where
#candidates=C large, #voters=V large, and, say, C=V^0.51.
That argument does not say anything about plurality winners, however.

I will now argue that the IRV winner is better than the plurality winner
(when they differ) slightly more than half the time in that puzzle's
limit-scenario,
albeit not necessarily "obviously better."

To explain my (somewhat nonrigorous given the lack of a definition,
but I still like it) reasoning behind that:
IRV ignores fewer ballot data than plurality but both ignore
asymptotically 100% of
the data on the ballots as is shown in puzzle 34A. The reason the plurality
winner is better than the IRV winner (in cases when it is) generally
arises from the parts of the ballots that both IRV and plurality
ignore. Since these ignored parts are asymptotically 100%, we can
expect the question "which is better -- IRV winner or plurality
winner?"
to have answer dominated by random noise in a random election (i.e.
regarding the ignored parts of the ballots as random and unknown,
while the parts that are not ignored are solid and known). Therefore
answer frequency should be near 50-50, with a bias in favor of IRV
which should diminish toward 0 in the limit.

--
Warren D. Smith
http://RangeVoting.org <-- add your endorsement (by clicking
"endorse" as 1st step)

[Ted Stern]

This page shows some simulations in a two-dimensional voting space:

http://zesty.ca/voting/sim/

The instability of IRV when two candidates are close together is quite evident.

Ted

--
You received this message because you are subscribed to the Google Groups "The Center for Election Science" group.
To unsubscribe from this group and stop receiving emails from it, send an email to electionscien...@googlegroups.com.
For more options, visit https://groups.google.com/d/optout.

[Clay Shentrup]

On Tuesday, August 18, 2015 at 11:26:26 AM UTC-7, Dodecatheon Meadia wrote:

This page shows some simulations in a two-dimensional voting space:

http://zesty.ca/voting/sim/

Incidentally, Ka-Ping Yee lives across the street from me at the other end of the block.

[Warren D Smith]

http://rangevoting.org/FreqIRVworsePlur.html

summarizes results on this question so far.