[EM] Scenario where IRV and Asset outperform Condorcet, Range, Bucklin, Approval.

[Jameson Quinn]

First off, I'm not generally an IRV advocate. But in the interests of
fairness, I think that the following (to me very plausible) 4-candidate
scenario should be considered.  I call it Radical Center, in honor of Thomas
Freidman's onanism. I'll present preferences, but you can make this work
with Approval (and thus also strategic Range or Bucklin) using reasonable
assumptions. In Approval and related systems, there is a safe defensive
strategy; in Condorcet systems, if both relevant groups use strategy,
neither wins and the whole society is stuck with significantly inferior
candidate.

Candidates are Left, Right, Moderate, and the eponymous Radical Center.

Honest preferences (6 voter groups split into 3 larger groups for easy
understanding.)
---(35 L>...>R leftists)---
18: L>M>RC>R
17: L>RC>M>R

---(30 ...>L=R centrists)---
16: M>RC>L=R
14: RC>M>L=R

---(35 R>...>L rightists)---
18: R>M>RC>L
17: R>RC>M>L

Condorcet winner is M. But if all the RC>M voters truncate before M, then M
does not beat R and L, so there's two cycles M>RC>R,L>M. Most Condorcet
tiebreakers, including Schulze and Minimax, would name RC as the winner. (Of
course, if the M voters retaliate in kind, then R or L would win Condorcet,
or M would win Approval, Range, or Bucklin.)

There are two ways I can see to avoid this dilemma. One is LNH-type
elimination, such as in IRV or certain versions of Asset. Since RC is
eliminated before M, no lower votes of the RC voters can help RC win.

The other way would be explicit "I'll support you if you support me" vote
types. Offhand, I know of no system which includes such votes. I imagine
that such systems do exist, and it would not be hard to invent one, but I
suspect that any such system would need ad-hoc rules and thus tend to do
poorly on criteria.

Food for thought,
JQ
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