[Election-Methods] YN model - simple voting model in which range optimal, others not

[Dave Ketchum]

On Sat, 29 Mar 2008 23:28:22 -0400 Abd ul-Rahman Lomax wrote:
> At 03:32 PM 3/29/2008, Dave Ketchum wrote:
> 
>> Some see forest; some see trees; who sees all?
> 
> 
> Those who see a forest made up of trees.
> 
>> Looking at the 31 voter Plurality example:
>>      16 voted for candidates with 3 or more Ys - but NONE for 4 Ys.
>>      9 voted for candidates with 3 or more Ns - 9 going all the way to 
>> 4 Ns.
>>
>> Seeing that as unbalanced, I inverted it.
> 
> 
> Which, of course, does nothing. Y and N are arbitrary. In the example, Y 
> means the majority position. Period.

Except, with complete inversion, N inherits majority position.
> 
> The example was not "balanced." It's a constructed example to show a 
> *possibility,* and, in case you haven't noticed, the general case for 
> actual election results is that they are not balanced. Now, is it 
> unreasonable that there was no voter preferring all Ys? Seems not. 
> However, consider this. Add a constant N to all voting patterns.

Agreed ANY collection of voters would be possible, but YN offers this 
collection as demonstrating what to expect from Plurality.

Actually Plurality is neutral as a method - a desirable feature.

Plurality's inadequacy, which causes us to look for better methods, 
involves limiting approval to a single candidate.  When faced with 
candidate collections such as Bush/Gore/Nader, voters sometimes wish to 
approve more than one as better than those they want to reject.
> 
> If this is done, then the difference between the all Y and the all N 
> pattern can be seen as merely the difference. I.e., there were 5 more 
> voters voting NNNN than voting YYYY. This is *quite* possible, and in a 
> large election, it would be just as possible as the reverse.
> 
>> You call the inversion unhelpful.  I agree with that as to quality of 
>> voting, but claim it is no worse than the original.  It does 
>> demonstrate the neutrality of Plurality for the same vote counts pick 
>> the winner.
> 
> 
> This is like saying that if we reverse all the votes, the winner 
> reverses. Sure. So?
> 
> It seems that Dave is persisting in assuming that the example is 
> supposed to be "typical" or something like that. It isn't. It is a 
> *possible* preference pattern among voters. If we have a near-tie on all 
> the issues, which would be, I'd think, somewhere around the center of 
> the bell-curve of possibilities, and if there are many voters, this 
> possibility is almost as likely as any other. (As to the result in the 
> presence of the "imbalance" Dave noted. However, the particular pattern 
> does involve other aspects not mentioned by him, in the incidence of the 
> *other* votes, other than the extremes).

I object to calling this example "likely" - think of such as 16 with 3 Ys 
together with ZERO 4 Ys.
> 
> However, not only does it seem probable that Dave would not understand 
> this, I'd guess he is not reading this at all, because he hasn't 
> responded to any of my explanations, only to Warren. So, would someone 
> who isn't filtered out by Dave be so kind as to explain this to him?

Tracing the filtering back to what you sent me on 23/3/08 at 2359, I 
assume it was unintentional, and will undo it.
> 
>> That each of these is possible is certainly true.
>>
>> As to preposterous, each is at least borderline, though they fit 
>> together well for showing extremes.
> 
> 
> As noted, the two cases are really the same case, just reversed *in 
> name.* Same logic. Same perverse result with Plurality, same 
> serendipitous result with Range.
> 
> To repeat the first situation:
> 
> For a set of four issues, naming the majority position on each issue as 
> Y, and with a field of candidates holding every possible combination of 
> positions (there are 16 such), and with 31 voters holding a particular 
> set of positions, it is possible that, with Plurality, the NNNN 
> candidate wins.
> 
> The second situation is the same as the first except the majority 
> position is named N. And then, with the particular pattern, that the 
> YYYY candidate wins.
> 
> In other words, Plurality can elect, under some conditions, a candidate 
> whose position on every issue is contrary to that of the majority.

Since Plurality echoes accurately what it is given as voters, its results 
simply respond to what it is given.
> 
> Isn't this interesting? Most of us would consider that, not merely a 
> poor result, but the worst possible result! The assumption is that the 
> voters vote sincerely. With that assumption, and an assumption that 
> votes are proportional to the extent of agreement, Range *always* 
> chooses the best possible result (again, it's an assumption that the 
> YYYY position is the best possible result, but a quite reasonable one).
> 
I did not attempt to analyze the quality of the Range analysis, but 
suspect that, based on what was done to Plurality.
> 
> 
> 
>> DWK
>>
>> On Fri, 28 Mar 2008 23:59:00 -0400 Abd ul-Rahman Lomax wrote:
>>
>>> At 10:02 PM 3/28/2008, you wrote:
>>>
>>>> Building on those thoughts, let's try something with Plurality:
>>>>       Start with that collection of voters and issues.
>>>>       Invert all the issues so that a Y will attract the same voters 
>>>> as an
>>>> N did, and an N will attract those who had gone for Y.
>>>>       Note that YYYY will now attract the same 5 voters who had gone for
>>>> NNNN, and the new NNNN will get 0 votes.
>>>>       The collection of voters, while owning no claims to randomness,
>>>> remain as legitimate as they had been.
>>>>
>>>> Making corresponding changes in tests of other methods should make
>>>> corresponding changes in their results.
>>>
>>>
>>> This accomplishes nothing. The arrangement was designed so that all 
>>> the issues, as stated, had a majority Yes votes. If you then invert 
>>> all the issues, the majority is No, and Plurality elects Yes.
>>> Dave, you really aren't getting it. The "simple voting model" shows 
>>> something quite simple: it is simplified, but it is not unreasonable, 
>>> it is actually *similar* to how voters actually decide whom to vote 
>>> for. (Voting models in use in sophisticated simulators use more 
>>> complex models, often with an N-dimensional "issue space," and issues 
>>> also include weights, weight being ignored in this -- except there 
>>> was a minor assumption about weight made in my conversion of the 
>>> issue relationships to sincere ranked ballots.)
>>> Then there is a particular constructed *example* which shows that 
>>> Plurality can elect the candidate who is opposed by the majority on 
>>> all the issues. They are different majorities; Plurality is 
>>> Majority-Criterion compliant, i.e., if there is a *single* majority 
>>> that prefers a candidate, and votes sincerely, that candidate must 
>>> win under Plurality.
>>> Ironically, this is not the case for Range, because of the 
>>> possibility that this majority casts weak votes. It's fairly easy to 
>>> show, however, that this is not a defect of Range, it is a defect in 
>>> the Majority Criterion, which neglects preference strength (which is 
>>> generally true of ranked ballot systems, which make a trivial 
>>> preference, where the voter really is pleased, say, with the election 
>>> of either of two different candidates, but does have some minor 
>>> preference, equal to and of the same effect as a life-or-death, happy 
>>> citizen vs. rebel or emigrant, kind of preference).
>>> Notice the assumption in the application of the model. Sincere 
>>> voting. This is a very important point. The criticism of Range by 
>>> those who actually know something about election methods is not that, 
>>> if voting is sincere, Range does poorly; it is actually known to be 
>>> an optimal method. With sincere votes. The charge is made, however, 
>>> that some voters will game the system, "exaggerating" their votes and 
>>> thereby gaining some personal advantage.
>>> While this view is incorrect, in my opinion, the reasons for that 
>>> aren't so simple. The basic point remains, and this is what the Y/N 
>>> model shows. With sincere votes, Range doesn't just win in that 
>>> constructed example. It chooses the majority Yes candidate in *all* 
>>> examples that can be constructed. Essentially, that's what it was 
>>> designed to do. Other methods will choose that candidate under some 
>>> conditions, but not all. That's the point. Exactly how often the bad 
>>> choice is made remains to be shown; Warren has done lots of 
>>> simulations, and his Bayesian Regret results for various methods do 
>>> estimate how often the results are suboptimal. Those were with 
>>> various kinds of voting models, and they were random assignments of 
>>> preferences and preference strengths to voters, *not* examples 
>>> constructed to produce some desired result.
>>> The example you looked at, with 31 voters, was designed to show a 
>>> *possible* outcome for Plurality. It was not pretended that this 
>>> would be a common preference pattern. I have seen no analysis, 
>>> though, that it is a preposterous pattern.
-- 
  davek at clarityconnect.com    people.clarityconnect.com/webpages3/davek
  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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