[EM] STAR

Fri Aug 18 13:50:22 PDT 2023

He posed a pizza choice among friends pronlem.. a problem of consensus as
opposed to "tyranny of the majority" ... how to find the best consensus
decision when a simple majority first place preference would not be ideal.

On Fri, Aug 18, 2023, 10:41 AM Colin Champion <
colin.champion at routemaster.app> wrote:

> Forest – I may be being slow, but... what problem are you trying to solve?
> The problem which fpdk (quite plausibly, to my mind) said was optimally
> solved by cardinal voting? Or the problem which I claimed was optimally
> solved by decision theory? Or something to do with tactical voting?
>    CJC
>
> On 18/08/2023 18:32, Forest Simmons wrote:
>
> It's been a while since I thought about this but here's something that
> somebody with some number crunching resources should experiment with ... a
> lottery method that I used to call "the ultimate lottery" back before Jobst
> invented MaxParC, which arguably has at least an equal claim to
> ultimateness:
>
> Ballots are positive homogeneous functions of the candidate probability
> variables. The homogeneity degree doesn't matter as long as all of the
> ballots are of the same degree.
>
> The candidate probabilities are chosen to maximize the product of the
> ballots.
>
> This candidate probability distribution can be realized as a spinner. The
> spinner is spun to determine the winner.
>
> How would this work for our pizza example?
>
> For example, each voter's ballot could be her pizza desirability [score]
> expectation as a function of the lottery probabilities.
>
> Then each A faction voter would submit the same ballot ... namely the
> function given by the expression
> 100pA+80pC, while each B faction voter would submit the expression
> 100pB+80pC.
>
> When these ballots are multiplied together, we get the product
> (100pA+80pC)^60×(100pB+80pC)^40.
>
> The p values that maximize this product (subject to the constraint that
> they are non-negative and sum to 100 percent) are pA=pB=0, and pC=100%.
>
> The lottery that maximizes the expectation product is called the Nash
> lottery after John Nash who first used this idea for efficient allocation
> of limited resources.
>
> Since expectations are linear combinations of the probabilities, they are
> homogeneous of degree one ... one person, on vote. Their product is
> homogeneous of degree n ... so n people, n votes.
>
> Instead of using voter expectations for their ballots, the voters could
> have used other homogeneous expressions ... for example, by simply
> replacing each sum of products by a max of the same products.
>
> The product of these modified ballots would be ...
>
> [max(100pA,80pC)]^60
> ×[max(100pB,80pC)]^40.
>
> Maximization of this product with the same constraints as before, yields
> the same consensus distribution ... pC=100%.
>
> This information is new in the sense that it has never been submitted for
> official publication ... it's an exclusive bonus of Rob Lanphier's EM list
> archive... first posted to this list back in 2011 after Jobst and I
> published our 2010 paper on the use of mixed strategies for achieving
> consensus.
>
> Anyway, it turns out that using the Max operator in place of the Sum
> operator yields a distribution with less entropy whenever the two
> distributions are not identical.
>
> Less entropy means less randomness, which means less chance, which in this
> context, means more consensus.
>
> In our example, the candidate distribution turned out to be 100 percent
> candidate C ... zero randomness ... zero entropy ... 100 percent consensus.
>
> Now you can see why I mentioned the need for number crunching capability
> ... experimenting with these ballot product maximizations requires some
> serious number crunching.
>
> The field is wide open. Is the Ultimate Lottery Method strongly monotonic?
> For that matter, how about even the Nash Lottery?
>
> Can MaxParC be formulated in terms of the Ultimate Lottery?
>
> Somebody with some grad students should get them going on this!
>
> fws
>
> On Thu, Aug 17, 2023, 11:10 AM Forest Simmons <forest.simmons21 at gmail.com>
> wrote:
>
>> 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.)
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>>>> info
>>>>
>>>
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