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

[Dave Ketchum]

On Sun, 30 Mar 2008 23:48:56 -0400 Abd ul-Rahman Lomax wrote:
> At 10:27 PM 3/30/2008, Dave Ketchum wrote:
> 
> 
>>Runoffs main value is recovering from a methods weaknesses until 
>>something can be done about the method.  They are too expensive to 
>>be accepted as if a normal part of a usable method.
> 
Below you first say I missed something, and then respond as if accepting.

Let's start with some Plurality results:
    27 red
    26 black
    24 yellow
    23 white

Thus a solid majority against each candidate.

Top-two runoff would get a majority of those who are willing to vote for 
either red or black - not likely to please a majority of voters.

IRV would have discarded white, who could be the best compromise.

Condorcet could have seen the same first choices, but also have seen 
second and third choices which would likely cause it to discard red and 
black, letting white vs yellow decide.
> 
> What is missed here is that the basic requirement for an election 
> method to be truly democratic is that the result actually be accepted 
> by a majority of those voting. Runoffs are a device for doing this, 
> and, as implemented, they are even better than they might seem, 
> though taking advantage of the facility is rare. In many runoffs, the 
> voter can write in a candidate, still. Thus it is theoretically 
> possible for another candidate than the top two to win. But with 
> Plurality, this trick is dangerous; only if there is a true majority 
> requirement, enforced through as many ballots as it takes, is there 
> real democracy. Anything short of that is a compromise.

While I strongly favor write-ins being doable, using them in runoffs can 
dangerously influences results.

"accepted by a majority of those voting"?  WRONG!  It is the community 
that needs satisfying - not just those actually voting but including the 
others eligible to vote and even those not eligible.
> 
> The problem is much more soluble than might appear. Elect 
> representatives, through methods that insure that everyone or almost 
> everyone is represented. Then the assembly of representatives elects 
> officers. Parliamentary system. Democratic. Note that the U.S. 
> started out with something like this, but it was corrupted and 
> perverted by the party system and the fact that the Constitutional 
> Convention just couldn't work out better rules for the selection of 
> electors. Further, not having proportional representation in the 
> House made it all the quirkier.
> 
This leaves deciding how to elect the representatives to be attended to.
> 
> 
>>>>I object to calling this example "likely" - think of such as 16 
>>>>with 3 Ys together with ZERO 4 Ys.
>>>
>>>Yes, but. Think of 100016 with 3 Ys together with 100000 with 4 Ys.
>>>That is, add 100000 to all position counts and thus to all vote 
>>>counts. The results are the same. It looks drastic because the 
>>>election has been boiled down to the *margins*.
>>>Note that if positions are random, we would expect 4 occurrences of 
>>>3Ys for every occurrence of 1 Y. It is like the number of 
>>>occurrences of coin toss patterns. If we throw a coin many times, 
>>>and count the occurrence of each sequence of four, we will get 
>>>these patterns of equal probability:
>>>YYYY
>>>YYYN
>>>YYNY
>>>YNYY
>>>NYYY
>>
>>Without arguing the exact validity of the above, the following 
>>combinations in the test case were stretching expectability:
>>     16 3Y with 0 4Y
>>     4 3N with 5 4N
>>
>>And, again, Plurality did not fail - it simply responded neutrally 
>>to the collection of votes.
> 
> 
> Plurality awards the win to the candidate with the most first place 
> votes, since that it all it detects. As shown, it is quite possible 
> that this candidate is not at all the best candidate, and that, in 
> fact, a majority of voters would agree.

We seem agreed we should move away from Plurality, though unable to agree 
on details.
> 
> What I wrote above was simple, and it addressed the exact situation 
> that Ketchum then responded with. The sequences I have were the 
> sequences with 3 and 4 Y votes; the point was that there were many 
> more 3Ys than 4Ys (i.e, 4 vs. 1) and this would hold with large 
> numbers of voters with random positions. Ketchum had asserted that 
> there was something unlikely about there being 4 and 0. And I pointed 
> out that this is actually only one vote different from the most 
> common pattern. The odd one is at the other end, where there are 4 3N 
> votes and 5 4N votes. The latter is five times the expected number. 
> But the sample is small and that kind of deviation would not be 
> terribly unlikely, and, if we see the scenario as being a reduction 
> by subtracting 100,000 votes from each total, what we really have is 
> an even distribution with very small deviations. (the deviations in 
> such a large sample would be expected to be larger than than, in fact.)
>                                                                                       
> But, again, the point was that the election is a possible one, not 
> that it was a probable one. It illustrates what *can* go wrong with 
> plurality, not what would *usually* go wrong.
> 
> It's really simple: to repeat, with sincere voting and a large field 
> of candidates covering all positions, Plurality is quite unreliable, 
> and this is known and seen in real elections. Because of the politics 
> of it all, plurality still works, usually. But definitely not 
> reliably. It can easily pick a candidate who would be rejected by a 
> large majority in favor of another candidate in the race.
> 
> 
>>One more time:  Plurality reports what the voters vote.
> 
> 
> That's kind of an oxymoron. All functioning election methods "report 
> what the voters vote," though some report more than others. Some 
> allow voters to express much more information, Plurality is about the 
> minimum possible.
> 
IRV is an example on the other side - looking at enough to satisfy its 
rules, and ignoring whatever else the voters say.
> 
>>>However, Range would always choose YYYY. It was *designed* to do that.
>>>Always. If voters vote sincerely.
>>
Range asks different information from voters.  I comment not beyond that here.

Condorcet asks the same information from voters as Plurality - for most 
voters most of the time that is adequate.  When voters feel need to 
express themselves more fully, Condorcet is willing to accept such to more 
fully respond to their desires.
      Note that there is debate as to whether the extra information 
Condorcet accepts (of the same better vs worse kind as in Plurality) is 
better or worse than the different extra for Range.
> 
> And Bucklin, at least in the example studied, likewise chooses YYYY, 
> whereas IRV, ranked according to certain assumptions, chose a 3Y 
> winner. Not bad, not optimal.

No comments on Bucklin at the moment.
-- 
  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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