[EM] Smith, FPP fails Minimal Defense and Clone-Winner

[Juho]

On Mar 11, 2010, at 11:41 PM, Kristofer Munsterhjelm wrote:

> Juho wrote:
>> On Mar 10, 2010, at 7:26 PM, Kristofer Munsterhjelm wrote:
>>> Juho wrote:
>
>>>> I'm not aware of any sequential candidate elimination based  
>>>> method that I'd be happy to recommend. One can however describe  
>>>> e.g. minmax(margins) in that way. Eliminate the candidate that is  
>>>> worst in the sense that it would need most additional votes to  
>>>> win others, then the next etc. In the elimination process one  
>>>> would consider also losses to candidates that have already been  
>>>> eliminated (I wonder if this approach makes it less "natural  
>>>> looking" than the elimination process of IRV).
>>>
>>> To my knowledge, Schulze-elimination is the same as basic Schulze.  
>>> In other words, if you run Schulze, eliminate the loser, run it  
>>> again, etc, you end up with the original result. That's not very  
>>> useful, but still...
>>>
>>> It might also be that any "full-blown candidate elimination  
>>> method" (you run the election as if the one that was eliminated  
>>> never stood) with a weighted positional base method (Borda,  
>>> Plurality, ...) is nonmonotonic. I can't prove it though!
>> One more addition to this elimination discussion. Maybe ability to  
>> give an ordering of the candidates is more important (and more  
>> generic) than using an elimination process. The preference graphs  
>> that many Condorcet methods use may not be as easy to understand to  
>> the voters as plain ordering is.
>> In principle single winner methods need not be able to produce any  
>> ordering of the candidates. It is enough to pick the single winner.  
>> But in order to make it easy to the voters and candidates to  
>> understand the results (and to explain e.g. how close some  
>> candidate was to winning the election) good and simple graphical  
>> and numeric information may be valuable in practical elections.
>
> Both of the advanced methods give an ordering, as do the obvious  
> ones (Minmax, least reversal, Copeland, second order 2-1- 
> Copeland...). They don't provide numerical information ("this close  
> to winning")

At least minmax(margins) does. It gives each candidate the number of  
additional votes that would guarantee victory to them. That is quite  
simple and could be used to e.g. provide information to the voters  
while the counting is in progress ("1000 votes still not counted, 100  
first preference votes would be enough to win"). Also a simple  
histogram would tell how each candidate is doing at the moment.

> , but that is hard: I read a paper about extending Schulze to do so,  
> and it used some rather complicated use of linear programming. Could  
> you sell that to the public? Not very likely, unless they happened  
> to be of the same kind that voted for the use of Meek in local New  
> Zealand elections.
>
>>>> (I have to add that if people want to keep the USA as it mostly  
>>>> is, a two party based system, then I must recommend FPTP :-). And  
>>>> if not, then maybe also some additional (maybe proportionality  
>>>> related) reforms are needed.)
>>>
>>> Wouldn't something like Condorcet multiwinner districts be better?  
>>> Pick a good Condorcet method and send the 5 first ranked on its  
>>> social ordering to the legislature. That would pick a bunch of  
>>> centrists (thus have "stability"), but it would pick the centrists  
>>> people actually wanted.
>>>
>>> Hm, that might not provide a true two-party system, though. One  
>>> could also have a "PR" system where the number of votes is  
>>> weighted so that parties with broad support gain superproportional  
>>> power, but then the question becomes why one should bother with  
>>> the PR at all.
>> Maybe Condorcet + single winner districts is a more stable  
>> approach. That combination makes a two-party system just somewhat  
>> softer, and allows the party structure (in individual districts) to  
>> evolve in time.
>> Another approach to systems between proportional representation and  
>> the two-party approach could be to have a proportional method but  
>> use districts with only very few representatives (2, 3,...). That  
>> would provide rough but in principle accurate proportionality and  
>> still give space only to few major parties. (Obviously my  
>> definition of full proportionality must be "with 1/n of the votes  
>> you will get one seat (where n = number of representatives)".)
>
> An interesting hybrid, I think (and I've mentioned it before), would  
> be to have a bicameral system where senators are elected according  
> to a statewide Condorcet method (pick a good centrist for each  
> state), and the House representatives are elected according to PR.

Yes, having also representatives that are non-partisan by nature could  
add something interesting and useful to an otherwise very party  
oriented and divided community.

(One could btw call this kind of representatives "widists" instead of  
"centrists" since Condorcet would pick a candidate with wide support  
instead of a candidate that is supported specifically by the centrist  
parties. Or maybe also term "centrist" has some similar meaning in  
addition to referring to the parties in the centre.)

>
> Having just a single from each state may be /too/ centrist, but to  
> pick two senators from each using a proportional ordering might work  
> - as long as it doesn't introduce partisan division.

This sounds a bit risky. An alternative approach would be to elect the  
single candidates from smaller areas and thereby increase their number  
and their locality. Local representatives would also be more tied to  
all the people that they are supposed to represent. If we go down to  
village level then all voters may know the representative personally  
and that candidate is also personally responsible to each one of them.

Juho