[Election-Methods] IRV-Tournament

[Dave Ketchum]

My points are that:
      Condorcet presents the SAME ballot rules to the voter as IRV - 
simply relaxed a trifle - a voter could vote by IRV rules, successfully.
      While Condorcet analyzes the ballot more like what would pass for 
tournament rules, it will usually agree with IRV as to winner:
           IRV cares only about front runners, discarding what it sees as 
the weakest of these and declaring the strongest remaining as winner.
           Condorcet compares every pair of candidates as in a tournament 
(how many A>B (A ranked and B ranked lower or not ranked) vs B>A (B ranked 
and A ranked lower or not ranked).  The candidate winning every one of its 
pairs is winner.  Front runners that IRV looks for are in a good position 
to win such a Condorcet tournament.

Carrying IRV's front runner emphasis to extremes, both would declare A the 
winner in the following:
      2 A
      1 B>A
      1 C>A
      3 D>A
      4 E>A
      10 F>A
      20 G>A  Point here is that this constructed pattern let A beat G 
21>20 by IRV rules, while many somewhat similar patterns would have let A 
win in Condorcet - which does not care if A is ever a front runner - only 
about its complete liking.

Implementing programming differs among these election methods - but they 
are not especially complex, beyond ability to read ranked voting, and 
voters need not worry about details.

IRV needs an array with a member for each candidate, counting front 
runners.  Once the least popular is identified, the ballots need 
recounting of who is front runners among those not yet discarded.

Condorcet needs an NxN matrix to count all the A>B and B>A values, but 
only needs to read each ballot one time for this.  Ok to read ballots into 
multiple matrices, such as one per precinct, for such can be summed into a 
result matrix.

SHOULD be of interest to voters that the matrix describes liking levels 
among all the pairs of candidates - useful for analysis and planning for 
future.

Condorcet cycles are near ties of three or more candidates such that each 
almost wins - A except for B>A, B except for C>B, and C except for A>C. 
Voters need to know this much, and programmers need to be able to defend 
their resolution to those voters asking for such.

-------- Original Message --------
Subject: Re: [Election-Methods] A Better Version of IRV?
To: EM <election-methods at lists.electorama.com>

On Sat, 12 Jul 2008 21:09:15 +0300 Juho wrote:
> On Jul 12, 2008, at 17:56 , Kristofer Munsterhjelm wrote:
> 
>> Dave Ketchum wrote:
>>
>>> Again, why NOT Condorcet?
>>> Its' ballot is ranking, essentially the same as IRV, except the  
>>> directions better be more intelligent:
>>>      Rank as many as you choose - ranking all is acceptable IF you  
>>> choose.
>>>      Rank as few as you choose - bullet voting is acceptable if  that 
>>> completes a voter's desired expression.
>>>      Equal ranking permitted.
>>> Condorcet usually awards the same winner as IRV.  Major differences:
>>>      Condorcet looks at ALL that the voters rank, while IRV  ignores 
>>> parts.
>>>      Condorcet recognizes near ties, and tries to respond  accordingly.
>>> Could be a debate about the near ties - would it be better to  
>>> resolve such with a runoff?  Runoffs take time and are expensive.   
>>> Are they enough better than what Condorcet can do with the  original 
>>> vote counts?
>>
>>
>> On technical merit alone, why not Condorcet indeed? But the thread  
>> was about momentum. In the situation where IRV can't be stopped,  what 
>> is the best way to nudge IRV towards something more desirable  while 
>> still keeping it IRV-ish enough that it'll retain the  momentum of 
>> "pure IRV"?
> 
I argue above that Condorcet, using the same ballot and usually finding 
the same winner, is about as close to IRV as could be reasonably asked.
> 
> One very simple approach would be to promote ranked methods as one  
> group. Just join the bandwagon, include all methods and leave the  
> details of the method to be decided later (pick the best then). The  
> delta from plurality to ranked methods and achieved improvements are  clear.
> 
>>
>> One modification that's been mentioned before is bottom two runoff  - 
>> eliminate the one of the two last placed that fewer prefer to the  
>> other. That would ensure a Condorcet winner always wins, but to  core 
>> IRV supporters, that's a weakness, because the Condorcet  winner could 
>> be a weak centrist. The ameliorated procedure would  also fail LNHarm.
>>
>> If the people on which the momentum is based would support any sort  
>> of elimination procedure, then I think Borda-elimination would be  
>> better; so what one really has to ask is, if IRV is unstoppable,  then 
>> how far from pure IRV can you go and still have it be IRV? IRV  with 
>> candidate withdrawal? IRV with candidate completion? BTR-IRV?  
>> Schwartz,IRV? Any sort of elimination system? Any sort of ranked  
>> ballot system?
>>
>>
>> One argument against Condorcet, which one may call half-technical,  is 
>> complexity. It's technical because it regards the method itself  and 
>> not whether Condorcet Winners are good winners (or similar),  and 
>> nontechnical because what's complex to a computer may not be  complex 
>> to a person and vice versa.

What the voter needs to know is not complex.  Debating how to resolve 
cycles is complex, but the implemented election method needs little more 
than that it should be rare and is a bit better than a lottery among 
almost equals.
      That the debating and implementing is a challenge, but the voters 
need not be concerned - except those who are gluttons for punishment.
>>
>> As far as complexity with regards to Condorcet goes, the good  
>> Condorcet methods are complex. Schulze may be easy to program (once  
>> you know the beatpath algorithm), but explaining beatpaths to the  
>> average voter is going to be hard. Copeland is easy but not very  good 
>> and ties a lot.
> 
> 
> Some Condorcet methods are simple, like minmax. It is good too. I  note 
> that you later referred to cloneproof methods as good methods.  Minmax 
> is not fully cloneproof but I don't think that is a problem.  (Same with 
> not being fully Condorcet loser compliant.)
> 
> If your favourite Condorcet method is complex then it may better  start 
> with promoting Condorcet methods in general. I think it is in  any case 
> a mistake to dive into the details of the methods when  promoting an 
> electoral reform. Citizens and politicians are simply  not interested in 
> such dives (would be counterproductive). Better to  use some more 
> general arguments that are linked to the reform needs  at more general 
> level.
> 
>>
>> One thing I've observed is that IRV focuses on how the process is  
>> done, while Condorcet methods focus on properties ("the winner is  the 
>> candidate which wins all one-on-one contests"). I'd say  explaining 
>> properties would be more easily understood than  explaining the 
>> process, but apparently this isn't a great  limitation for IRV, given 
>> its momentum so far.
> 
> 
> IRV is typically described as it it was a "public fight" between  
> candidates where the candidates are eliminated one at a time. This is  a 
> very appealing style because of the very real life like and exiting  
> image it offers. The description also sounds quite fair (at least at  
> first sight).

So I listened to those who call Condorcet a tournament with the winner 
winning the election.
> 
> There are also differences in how different Condorcet methods are  
> described. To me methods that are justified using (possibly long)  beat 
> paths are philosophically different from methods that are based  on 
> evaluating the more local properties of individual candidates  (e.g. 
> minmax).
> 
> (Also the philosophy of finding a complete ordering of the candidates  
> is different from the philosophy of just identifying the best  candidate 
> without establishing a complete order. The interesting  point is that 
> individual preferences of the voters are usually  expected to linear 
> while it is known that group opinions may well be  cyclic (just a 
> natural property, not a fault that should be somehow  corrected).)
> 
Doing complete ordering has to be more complex than finding a single winner.

Cycling is natural, but only matters when candidates are near enough to a 
tie to make it possible.
>>
>> Perhaps Ranked Pairs would have a chance? It's one of the better  
>> Condorcet methods (cloneproof, etc), and if people accept the  
>> pairwise comparison idea, it should follow quite easily. Say  
>> something like that you can't please everyone all the time, so  please 
>> most, which is to say that one locks preferences in the  order of 
>> greatest victories first. Then anyone complaining because  his group's 
>> (cyclic) preference was not locked could be rebutted by  a larger 
>> group saying that if it had been, more people (namely,  that larger 
>> group) would have been overridden. Here you have both  method 
>> (locking) and properties (group complaint "immunity"), as well.
>>
>> It'd be interesting to investigate which simple or intuitive  methods 
>> are the best. I don't know what would constitute simple to  voters, 
>> perhaps "Of those candidates that [some statement], choose  the one 
>> that [some statement]", or "[Somehow reduce the set of  candidates] 
>> until [criterion is met], then that one is the winner"  for various 
>> sentence parts inside the brackets. Those are all  method-based 
>> explanations; maybe property-based ones would be  better. If the voter 
>> trusts that the method does what the property  says, and the property 
>> is desirable, then that could be the case.
> 
> 
> I'll continue my "minmax campaign" a bit more. The best part of minmax 
> (margins) (and the reason why I'm interested in it) is that it has a  
> very natural (and easy to understand) description and justification.  It 
> elects the candidate that needs the least number of additional  votes 
> (if any) to win each of the other candidates (in pairwise  comparisons). 
> I'd say that is a reasonably good description of a  candidate that 
> deserves to win (if one is looking for a good  compromise candidate).

Methods for resolving cycles are important, but are best left as a detail 
to be debated AFTER resolving the other major details.
> 
> Juho
-- 
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  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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