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

[Abd ul-Rahman Lomax]

At 03:22 PM 5/12/2010, Jameson Quinn wrote:
>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.

I generally have a problem with analyses like this. The setup did 
seem plausible at first glance; it's basically a linear spectrum, 
except the leftists and the rightists are split on whether or not M 
is to the left of RC or to the right of RC. That's very odd.

This is what I get from it: the utility difference between M and RC 
is very low, to the leftists and rightists. This does imply, to some 
degree, that these candidates will be close to each other even for 
their own supporters. This is supported by the equal-bottom ranking 
of left and right candidates.

The problem is that without utility analysis, i.e., without plausible 
underlying utility profiles, whether an outcome is "safe" or not is 
pretty much a guess, and the comment "significantly inferior" is 
without foundation.

The concern here is whether or not M or RC win (with a small concern 
about whether or not R or L win, which is possible if all voters 
truncate, that's a plurality result, it could, of course, happen 
under Range or Approval or Bucklin if voters do nearly all truncate. 
However, if a majority is required, the election would fail. The 
question then is who gets into a runoff, if there is elimination. 
That would depend on the primary method and the runoff rules, it 
should not be assumed that it would be top two runoff.

>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

What is a reasonable assumption for average utilities, if these are 
sincere preferences, and if they represent significant preference 
strength? Given the perception of the centrists regarding the L and R 
candidates (which is very odd, there would normally be some centrists 
who would prefer left to right and vice-versa), I will assume that 
the distance between left and center and center and right is high. 
Otherwise there would be more bias in the preferences; as it is, they 
a e almost equal.

I'm coming to the conclusion that this scenario is about two clones, 
basically, candidates so close to each other that the voting for them 
is very noisy. It's very odd that the centrists are equal-bottom 
ranking, but that none of the leftists or rightists equal middle-rank 
the centrists.

Defective example, not plausible, my conclusion.

Without doing a utility study (i.e., making some assumptions about 
utility patterns that would explain the preferences), what I see 
indicates to me that the social utility difference between M and RC 
winning is minor. M has a small edge in first preference votes, but 
the right and the left prefer M by an insignificant margin.

The example shows to me why requiring a majority is wise. If voters 
truncate, which they should be allowed to do, particularly in a 
primary, it will cause majority failure, and this is only a problem 
if the method for handling the runoff is defective. Top Two Runoff, 
with vote-for-one in the primary, is the method here that ends up 
with a runoff between L and R, which, if the preferences are sincere, 
is a dead heat tie, because the centrists won't bother voting. They 
don't care, right? I think that's a contradiction in the setup.

As a single-ballot method, Bucklin would be quite likely to get this 
one right, unless the "centrists" are truly "my candidate or else" 
partisans, which isn't normally how centrists think.... But suppose 
they did, what would happen? I'm just stating two-round Bucklin for simplicity.

18 L>M
17 L>RC
16 M
14 RC
18 R>M
17 R>RC

or

35 L>M=RC
16 M
14 RC
35 R>M=RC

No majority in the first rank, so add in the seconds.

first scenario  second scenario
L:35            L:35
M:52            M:86
RC:48           RC:84
R:35            R:35

This results in M winning, but the variability could flip it to RC 
easily. The R and L factions are exposed as exclusive, they have no 
marginal support outside their own faction.

This is the game they face: R and L could also truncate. Suppose they 
all truncate. (It can be done better, there could is a way to coax 
some intermediate preference expression out of the L and R voters 
that could be used to set up better runoff conditions). They have a 
toss-up. They might win, great! But they might lose as well, and if 
they know the situation, they could see that one voter failing to 
make it to the polls or making a mistake or whatever could award the 
victory to the worst candidate, from their perspsective. That's an 
average utility of zero (in a +/- scale). If we assume from their 
preferences that they do have some above-zero utility for their 
preferred middle candidate, they increase their likely outcome by 
adding a lower preference vote for one or both centrists; in the 
first scenario above I had them vote for only one, then for both in 
the second scenario.

M wins in both scenarios. Single-round Bucklin would be likely to 
award this to M or RC, it's close. Voters do not respond well to 
Machiavellian plots to kill the chances of a candidate whom the 
voters see as being almost as good as their favorite, and if their 
favorite urges them to do this, it could be political suicide.

Political activists don't necessarily think this way, which is why 
political activists often do very badly predicting the behavior of 
voters, who do not like to see factions treat them as if they were property.

In reality, voters do not fit into neat factions, their preference 
profiles are spread. I think it would be pretty unlikely to find a 
scenario like the one described using simulations based on issue 
space distances.