[EM] STAR

[Forest Simmons]

Suppose voter utilities for three kinds of pizza are

60 A[100]>C[80]>>B[0]
40 B[100]>C[80]>>A[0]

Suppose the voters must choose by majority choice between pizza C and the
favorite pizza of a voter to be determined by randomly drawing a voter name
from a hat.

The random drawing method would give voter utility expectations of

60%100+40%0 for each A groupie, and
40%100+60%0 for each B groupie.

The max utility expectation would be 60.

On the other hand, if voters decide to go with the sure deal C, the assured
utility fo every voter will be 80.

Every rational voter faced with this choice will choose C.

Here we have an ostensibly random method that is sure to yield a consensus
decision when voters vote ratkonally.

More on this topic at

https://www.researchgate.net/figure/Properties-of-common-group-decision-methods-Nash-Lottery-and-MaxParC-Solid-and-dashed_fig3_342120971


fws

On Thu, Aug 17, 2023, 1:18 AM Forest Simmons <forest.simmons21 at gmail.com>
wrote:

> The best methods that I know of for the friends context are minimum
> entropy lottery methods characterized by max possible consensus (min
> entropy) consistent with a proportional lottery method with higher entropy
> fallback to disincentivize  gratuitous defection.
>
> Jobst's MaxParC (Max Partial Consensus) is the best example.
>
> Too late to elaborate tonight.
>
> fws
>
> I'll
>
> On Wed, Aug 16, 2023, 10:01 AM <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)
>>
>> > 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
>>
>> "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.)
>> ----
>> Election-Methods mailing list - see https://electorama.com/em for list
>> info
>>
>
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