[EM] Response to critique of MJ (MCA subtype) procedure by Felsenthal & Mac

[Jameson Quinn]

2011/3/1 Warren Smith <warren.wds at gmail.com>

> Jameson Quinn says
> "the objection that 'Seriously nonmajoritarian results are possible if
> most preferences between two candidates do not straddle the median' is
> easily addressed by offering only 3 rating levels."
>
> It seems to me however, that MJ with 3 levels would in practice usually
> yield
> an N-way tie with every candidate median-rated "middle,"


Two responses:
1. I don't agree. Specifically, in an election with two correctly-known
frontrunners and almost all voters using the simple heuristic of approving
only one of them - which would describe at least a substantial fraction, and
I believe a majority, of elections - only one of them, the true pairwise
champion, would have a median rating above bottom. This by no means exhausts
the possibilities for a clear winner.
2. Anyway, even if "usually" were true, a system which is sometimes
equivalent and sometimes superior is a system which is superior.

> whereupon the
> Balinski+Laraki
> tiebreak procedure would reduce to "elect the candidate with the most
> top-ratings"
> otherwise known, basically, as "approval voting."
>
Also not true. Say there are two candidates:
A: 20 preferred, 50 approved, 30 unapproved
B: 10 preferred, 80 approved, 10 unapproved
B, with fewer top ratings, wins, when eliminating 40 median votes shifts A's
adjusted median rating down to unapproved.
Actually, I think that "fewer unapproved" would be the determining factor *
more* often than "more preferred", because people will tend to vote more
candidates as unapproved than as preferred.
Sure, you could argue that this result is still isomorphic to approval
voting, but that would be switching your isomorphism. The point is that CJ
is clearly collecting and using more data than approval voting.


> You may be amused by the following snooty email I sent to Felsenthal &
> Machover.


As you know, I agree with many of the substantive arguments you made there,
and disagree with some others. In particular, unlike you, I believe that a
mix of strategic and honest voters would create real-world problems for
range (occasionally in terms of results, when two factions used strategy
unevenly; and universally in terms of post-result sore losers, who would
eventually be able to use this as an excuse to repeal).

But as for the snootiness... of course, I would have expressed it
differently, but I have to agree with the sentiment. Publishing a paper on
voting without being substantially aware of the non-academic (internet) work
on voting theory is like writing a paper on theology today after only
reviewing the prior work in Latin. F+M may find citations, but they're not
really on the cutting edge.

Jameson
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