[EM] STAR

[Colin Champion]

I think that bringing cardinal voting into the discussion is a red herring.
    My contention is as follows. Suppose that we are given a set of 
ballots (eg. a set of rankings of candidates) and an adequetely 
specified generative model (eg. a jury model or a spatial model). Then 
there is a mathematically identifiable rightful winner (I shall give an 
example in a moment). The fact that given additional information (eg. 
cardinal preferences) we might prefer a different candidate is 
irrelevant - it is a question of there being a valid statistical 
inference from the information given.
    We might also consider the question of which is the best candidate 
sub specie aeternitatis. This seems to me equally irrelevant. If there 
exists such as thing as an objectively best candidate, then what makes 
him objectively best is nothing to do with the voters' opinions.

Example of identifying the rightful winner: let the ballots come from a 
Gaussian jury model. The candidates have valences (merits) drawn from a 
standard univariate Gaussian, and each voter's assessment of the valence 
of each candidate is a noisy estimate of the true merit, obtained by 
adding an iid N(0,sigma) noise term to the true valence. A perfect 
voting method will elect the candidate whose posterior expected valence 
is greatest. This is a well defined and soluble mathematical problem.

CJC

On 16/08/2023 17:52, fdpk69p6uq at snkmail.com wrote:
>
> On Mon, Aug 14, 2023 at 12:09 AM C.Benham wrote:
>
>     >   I think this is an interesting point. We can ask at a
>     philosophical level what makes a good voting method. Is it just
>     one that ticks the most boxes, or is it one that most reliably
>     gets the "best" result?
>
>
> The one that most reliably gets the best result in the real world. The 
> difficulty with this approach is accurately modeling human voting 
> behavior and the consequent utility experienced from the winner, but 
> it's still the better answer philosophically.
>
> (Note that VSE predates Jameson Quinn by decades, and has had several 
> different names: 
> https://en.wikipedia.org/wiki/Social_utility_efficiency 
> <https://en.wikipedia.org/wiki/Social_utility_efficiency>)
>
>     > And that's partly because the premise of Condorcet is
>     essentially built on a logical fallacy - basically that if A is
>     preferred to B on more ballots that vice versa then electing A must
>     > be a better result than electing B.
>
>     I'd be interested in reading your explanation of why you think
>     that is a
>     "logical fallacy".  What about if there are only two candidates?
>
>
> Ranked ballots can't capture strength of preference. It's possible for 
> a majority-preferred candidate to be very polarizing (loved by 51% and 
> hated by 49%), while the minority-preferred candidate is broadly-liked 
> and has a much higher overall approval/favorability rating.  Which 
> candidate is the rightful winner?
>
> https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html 
> <https://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html>
>
> "Suppose you and a pair of friends are looking to order a pizza. You, 
> and one friend, really like mushrooms, and prefer them over all other 
> vegetable options, but you both also really, /really/ like pepperoni. 
> Your other friend also really likes mushrooms, and prefers them over 
> all other options, but they're also vegetarian. What one topping 
> should you get?
>
> Clearly the answer is mushrooms, and there is no group of friends 
> worth calling themselves such who would conclude otherwise. It's so 
> obvious that it hardly seems worth calling attention to. So why is it, 
> that if we put this decision up to a vote, do so many election 
> methods, which are otherwise seen as perfectly reasonable methods, 
> fail? Plurality, top-two runoffs 
> <http://en.wikipedia.org/wiki/Two-round_system>, instant runoff voting 
> <http://en.wikipedia.org/wiki/Instant-runoff_voting>, all variations 
> of Condorcet's method <http://en.wikipedia.org/wiki/Condorcet_method>, 
> even Bucklin voting <http://en.wikipedia.org/wiki/Bucklin_voting>; all 
> of them, incorrectly, choose pepperoni."
>
> (And strength of preference is clearly a real thing in our brains.  If 
> you prefer A > B > C, and are given the choice between Box 1, which 
> contains B, and Box 2, which has a 50/50 chance of containing A or C, 
> which do you choose?  What if the probability were 1 in a million of 
> Box 2 containing C?  By varying the probability until it's impossible 
> to decide, you can measure the relative strength of preference for B > 
> C vs A > C.)
>
> ----
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