[EM] [CES #4445] Re: Looking at Condorcet

[Juho Laatu]

On 5.2.2012, at 5.34, robert bristow-johnson wrote:

> On 2/4/12 4:01 PM, Juho Laatu wrote:
>> On 4.2.2012, at 19.14, robert bristow-johnson wrote:
>> 
>>> so, i have a few questions for everyone here:
>>> 
>>>    1.  do we all agree that every voter's franchise is precisely equal?
>>>    2.  if each voter's franchise is equal, should we expect any voter
>>>        that has an opinion regarding the candidates/choices to
>>>        voluntarily dilute the weight or effectiveness of their vote,
>>>        even if their preference is weak?
>>>    3.  so, based on the answers to 1 and 2, if there is an election or
>>>        choice between only two alternatives (yes/no) or two candidates,
>>>        that this election be decided any differently than, as we
>>>        were told in elementary school, the "simple majority" with
>>>        "one person, one vote"?
>> My generic answer is that there is no single answer to how single-winner decisions should be made. Different elections may have different targets.
>> 
>> In some elections / decision making processes people may voluntary dilute their vote. This approach typically means that the election is non-competitive.
>> The properties of the environment, like competitiveness set some limits to what election methods can be used.
> 
> i've been assuming it's a governmental election and that it's competitive.  if it's not competitive, then it's either not important enough for voters to have a stake in the outcome, or there is little choice and everybody is pretty much in agreement.  even in the latter case, given the original restriction in (3.) that it's two candidates or two choices and that one of those two choices must be made by some deadline (normally Election Day), what situation can you think of, Juho, where the decision-making rule would be anything other than the simple majority of equally-weighted votes?

Ok, since we are talking about typical governmentale elections, we can assume that the environment is competitive. We may also assume (in governmental elections) that voters do have lots of information on the candidates and current situation (polls). This information means that dilution due to uncertainty (e.g. zero information) is not a typical voting pattern. We may now maybe safely assume that the main rule is that voters will not dilue their vote. If we further assume that we are talking about elections where the one-man-one-vote principle applies (part of the targets), then it seems that we are indeed talking about majority elections. One more assumption on the targets was that we want the election to be deterministic (i.e. e.g. random vote will not do), and we wanted the method to make the decision (i.e. not be inconclusive). Full ties can however be be solved using lottery. Probably we also wanted a method where the final decision is made by the first set of voters, i.e. there is no delegation of decision making power to some next level of decision makers.

> 
> 
>>  Another criterion to what election method to use is how well each election method implements the targets of the election. The choice of the election method and collected information in the ballots thus depend on the targets and the environment. (Strategies could be seen to depend on the properties of the envionment and on how well a method can implement the targets in this environment.)
>> 
>> I'll expand the pizza example a bit to demonstrate that there is a rich set of possible targets and ballot information. When a group of friends decides on which pizza to take or where to eat they quite often (unconciously) use a model where the range of opinions is not from 0 to max, but from minus infinity to plus infinity.
> i'm sure that works really well when the mean-metric is used.  problem is, my opinion of George W Bush (-infinity) outweighs the opinions of all those who voted for him.  or maybe not.

Yes, -inf overrules any number of positive votes, except the +inf vote. That means that the inf votes can only be used in elections that are not fully competitive.

> 
>>  The scale has some fixed points that are linked to natual language. Such points can be "excellent", "not my favourite" and "pretty much unacceptable". Vote -inf means "impossible". Vote +inf means "the only possible alternative". With these values the outcome of the election / decision making process may be undecided (if two alternatives get +inf, or if some alternative gets both -inf and +inf, or if all alternatives get -inf).
> 
> so is undecisiveness a useful property for governmental elections?

Some governmental elections may be inconclusive. We may for example require certain number of voters to participate, or we may require supermajority. Supermajority offers us some hyteresis in the decision making process. The inf values will probably not be used in governmental (general) elections.

> 
>> My answer thus is that in all three questions there can be different options. If someone asks me what single-winner method should be used, I'll probably ask what the targets and the environment are.
> 
> the environmental is: governmental election, two competitive choices (yes or no on a ballot question, Romney vs. Obama, whatever).  it's not just pizza and the other voters are myriad and not necessarily friends.  but, even so, you and the other voters that aren't your friends have to all live with the result.  so: Two-choices, Competitive, Governmental (stakes are high), Decisive (decision must be made by Election Day).

Ok, I guess I managed to assume these ones.

The high number of voters makes the environment more unpredictable and uncontrollable, although maybe statistically easier to estimate. A typical additional assumprtion in governmental elections is also independent decision making among the voters, i.e. they are not puppets that are controlled by some key people, organization or by some well known voting habits or patterns (=> e.g. no generally followed recommendations on how to fill the ballot). These properties have some impact on what strategies one can expect to be used, and therefore on what election methods one can and should use.

> 
> how're you going to do it?  now those conditions are externally forced but we'll add one more that we wouldn't have to, but we do because it's fair: Equally weighted franchise.  (if it's not equal, how do you decide whose votes "are more equal than others"?)  so your environment and targets are constrained by all those conditions.  what decision rule, other than the simple majority of equally weighted votes can you (or anybody) justify?

Yes, equal votes is a typical requirement. And yes, we have now pretty much bound ourselves to majority decisions (even if the method was something like Range).

> 
>>  A good definition of the targets should be detailed enough to allow also e.g. understanding what relevant information one expects the voters to have and express.
> 
> we'll get to that later (with the multi-candidate race), but what i am first trying to settle is something more fundamental.
> 
>>  The targets should also tell what alternative would be a good choice.
> 
> sorry, i don't understand tangibly what you mean here.

Maybe we have now implicitly said that in a competition between two candidates we actually want to elect a candidate that is the favourite of majority of the voters. We do not care if the losing side is a bit more desperate because of losing the election than the now winning side would be if they would lose.

Or alternatively we might thnk that actually it would be good to elect the other candidate, but because of the constraints (e.g. strategic voting), we were forced to use a majority based method. The chosen method is however the best we could find under these conditions.

(In some more complex set-up the definition of a good winner could be more fine-tuned. We might for example agree that we would like the outcome to be reasonably good also for the most disappointed satisfied voters. I.e. we are close to the approach of maximizing the worst outcome.)

> 
>>  With information like this it should be (in principle) a quite mechanical process to check all relevant available methods against the targets and environment description, and then pick the best method (and ballot format) (and guidance to the voters on how to vote).
> 
> really?  okay so, with a simple well-defined environment: Two-choice question, Competitive interests, High stakes, Decisive deadline, and Equal franchise for every voter; then what further questions need be settled to adopt a ballot format, tabulation method, and voter instructions?

Yes, in theory this process could be close to mechanical. In this particular case we pretty much narrowed the choice of methods to a set of methods that all elect the majoity winner in the case that there are only two candidates.

Juho



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