[EM] STAR

Fri Aug 18 17:01:49 PDT 2023

That's pretty good ... not too bad for a deterministic method, if in a good
faith, no pressure context.

Some people would resort to sortition, especially if the decision is one
that arises frequently ... every Friday, say.

Other  lottery methods exist that reduce the amount of randomness (the
entropy) but remain proportional (like random ballot).

During a  ten year period winding down in 2015, Jobst and I intensively
explored how much you can limit entropy (maximize the degree of consensus)
under the constraint of minimal acceptable fairness ... which for us was
the same kind of long term proportionality that random ballot favorite
would ensure ... so min randomness required for proportional fairness ...
or expressed differently ... max consensus with zero sacrifice  of strict
statistically proportional representation.

Our exploration culminated in Jobst's invention of MaxParC , a Maximum
Partial Consensus method based on ballots where the voters specify (for
each alternative) how many other voters would have to be on board before
they would be willing to join with them in support of that alternative.

>From that information you can easily figure out which alternative has the
potential for the most partial consensus... and that option will be awarded
a lottery probability in proportion to that max potential support ... etc.

That's the best known solution for maximising consensus without
compromising proportional fairness.

But in any context where MaxParC would give 100 percent consensus, there is
always a simpler lottery method that would ensure the same result among
rational voters who are already aware of the other voters' preferences ...
so they don't need to fill out MaxParC ballots.

If rational, well informed voters already know among themselves that at
least one candidate is a shoo-in for neing a 100 percent implicit approval
winner (or a 100 percent consensus MaxParC winner), then a score ballot is
all we need ...

... among the candidates with 100 percent implicit approval, elect the one
with the greatest score total.

The projected MaxParC winner C should be among those 100 percent Implici
Approval candidates.

However, if (by some rare fluke) neither C nor any other candidate
amassed100 percent implicit approval, then the winner must be chosen by
random ballot favorite, in order to ensure fair proportionality.

Does that seem to make sense?

fws

On Fri, Aug 18, 2023, 1:58 PM Colin Champion <colin.champion at routemaster.app>
wrote:

> Forest - I read fpdk's post as an implicit argument for cardinal voting
> (which was why it was relevant to STAR). Each friend states the utility of
> each topping to himself or herself: which topping do they choose
> collectively? And the answer is the one whose sum of utilities is greatest.
> I don't think there's a better answer.
>    CJC
>
> On 18/08/2023 21:50, Forest Simmons wrote:
>
> 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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>>>>> list info
>>>>>
>>>>
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