[EM] Range vs Condorcet Overview

[Jobst Heitzig]

Dear Greg,

I appreciate your trying to sum up the recent discussion. Some remarks:

You wrote:
> Range Voting:
> 
> There are two types of arguments against this system:

There is another one - in my opinion the most serious problem of Range 
Voting: It fails to achieve exactly that which it claims to be designed 
to achieve, namely the maximization of social utility (or, if you like, 
the minimization of Bayesian regret). Just look at the following very 
simple and common situation of two factions and a good compromise option:

55% of voters have these utilities: A 100, C 80, B 0
45% of voters have these utilities: B 100, C 80, A 0

Obviously, utilitarians would want C to win, but A will be elected most 
certainly under Range (as under any other majoritarian method including 
Condorcet methods, but Condorcet methods don't claim to maximize social 
utility).

> 1)      Ratings themselves are useless/unreasonable/illogical/not 
> indicative of reality

My point was not that they are useless/unreasonable/illogical/not
indicative of reality but that we may not assume that a typical voter 
can easily come up with a meaningful set of ratings! Even if there were 
a working definition of the meaning of a rating in terms of happiness 
levels measured biochemically or in whatever way, it would still be 
practically impossible to come up with more than a very vague assignment 
of ratings. I wonder if any supporter of ratings has really ever 
honestly asked himself whether he can justify why he has assigned to 
some option a rating of, say, 61 instead of 62 on a scale from 0 to 100. 
  I doubt it!

> a.       The concept of comparing candidates along a single dimension is 
> more intuitive and hence more meaningful to voters than making O(n^2) 
> binary decisions

Is there any scientific evidence to support this claim? For me it is 
surely a simpler task to answer questions of the sort "do you prefer A 
or B?" than to answer questions of the sort "where would you place A, B, 
and C along an interval from 0 to 100?", even more so when no indication 
is given as to what these numbers are supposed to mean.

> a.       Does zero-info in this case mean a) lack of info about of the 
> behavior of other voters or b) (a) and lack of info about other 
> candidates as well? Either way, if the problem can be ameliorated by 
> adding info, then add info.

Nice idea. Perhaps you could tell us how this should be done when at the 
same time votes are secret? Or do you suggest vote secrecy is not necessary?

> b.      Is this behavior even a good thing? If the majority isn't 
> exercising its influence and a compromise candidate is elected instead, 
> do you really want a polarizing candidate or a compromise one?

At least to utilitarians that should be obvious: If the compromise is a 
good one (leading to more social utility than the polarizing ones), he 
should clearly be the winner. There are methods which make this highly 
probable since they are not majoritarian methods.

> RP:
> 
> 1)      This is a system I initially cited as an example of a reasonable 
> Condorcet method, it hasn't really been argued about.

At least not recently. One problem with RP (as with Beatpath aka 
Schulze) is that they fail Independence of Pareto Dominated 
Alternatives: adding a clearly bad candidate - in this case one to which 
some other candidate is preferred by each and every voter - should have 
no impact on the result. But with RP and Beatpath such a candidacy can 
affect the result while with River it cannot.

> Framing the debate:
> 
> Debating the specific merits of Range Voting or Condorcet Method X is 
> meaningless unless we can agree on some kind of metric.

No. Assuming there would be a single metric that summarizes all the 
conflicting goals and criteria one can rightly ask for in an election 
method is just as wrong as assuming voters can always place options on a 
single dimension. There is just no evidence for either claim but plenty 
of evidence against them.

> Debates about which properties are important don't really lead anywhere. 
> There are a few we can probably agree upon. Let's see how often it 
> satisfies those properties. I advocate moving away from a binary 
> framework and focusing on how often certain properties are satisfied.
> 
> I like the Bayesian Regret metric because it's nice and quantifiable. 

Loving quantifiable things is among the worst diseases in science. As a 
mathematician I know what I'm talking about here. As long as there is no 
evidence that some notion is quantifiable, the safe assumption is always 
to assume that it is *not* quantifiable, or at least not quantifiable in 
a *single* dimension. So, let me again suggest that we try to work based 
on evidence and not on wishful thinking.

Yours, Jobst

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