[EM] [ESF #1100] Re: [RangeVoting] Scenario where IRV and Asset outperform Condorcet, Range, Bucklin, Approval.

[Jameson Quinn]

2010/5/12 Abd ul-Rahman Lomax <abd at lomaxdesign.com>

> 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.
>

The equal-bottom of the centrists is solely to save typing. Of course in
real life the centrists would be somewhat to one side or the other. The
point is that the two centrist candidates are equally centrist, but differ
on some other dimension.


>
> Defective example, not plausible, my conclusion.
>

I could come up with any number of slight variations. The point is not to
nitpick every detail, it's to see the scenario as a simplified case of a
range of plausible scenarios. Say that voters are normally distributed over
X and Y with SD 1 and .5, and the candidates are at L=(-2,0); M=(0,0);
RC=(0,0.1); R=(2,0).

>
> 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.


But not if RC voters truncate but M voters don't. As I said, in
approval/Bucklin/range, there is an effective defense. Strategy is still a
problem for expressivity, divisiveness and extrapartisan bias, and
legitimacy (of the winner and of the system.) Again, not the end of the
world.


> 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.
>

Unsubstantiated. So let me respond in kind: The scenario assumes that R and
L are highly polarizing candidates, so the M voters, true moderates, are
unwilling to risk either one, and so don't truncate; while the RC voters
have some irrational or selfish beef with M, so do. If the call to truncate
is seen as principled and not strategic - and it could be - it would cause
less backlash.

>
> 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.
>
> Wanna bet?

Look. It's a scenario. It's not totally implausible. We are blowing hot air
if we argue too much about how plausible it is. A system that deals with it
well is better than a system which doesn't, all other things being equal.
All other things are never equal, so it's just one factor among many.

I am planning to one day make a program which explores how likely and how
severe strategic opportunities are in each system. Typifying such strategic
opportunities is useful prior work.

JQ
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