[EM] Ordering defeats in Minimax

[Kristofer Munsterhjelm]

On 05/07/2017 10:58 AM, Juho Laatu wrote:
>> On 06 May 2017, at 23:26, Kevin Venzke <stepjak at yahoo.fr
>> <mailto:stepjak at yahoo.fr>> wrote:

>> Legislators usually don't use election
>> methods. I would say essentially they figure out among themselves what
>> the outcome likely must be and then "elect" it, typically by a majority
>> vote. If voters could do that directly I think that would be the ideal
>> situation, as far as minimizing the need for strategy.
>
> That's an interesting viewpoint. I'd like to see Condorcet tested in
> some parliaments. Although negotiations and Plurality can be used to
> solve many cases, also Condorcet and the idea of having multiple
> candidates could have some benefits. The first one in my mind is
> openness. Even when the "big boys" have agreed something behind the
> screens, and then bring that decision into a majority vote, some smaller
> groupings could add some alternatives in the election that they consider
> better. This would open up the available alternatives to the world
> (media, public), and all voters would have to take position on the
> presented alternatives. Small parties or groupings could thus make
> sensible compromise proposals that might even win, if they are good enough.

I think some parliaments use the following procedure for multiple 
proposals or amendments:

Some group decides the agenda (I'm not sure who; it probably depends on 
the parliament in question).

Then the parliament discusses the first two options, and does a majority 
vote between the two. It then does a majority vote between the winner so 
far and the next option, and so on until all options have been 
considered. The winner at the end of the procedure is the option that is 
accepted.

This method is Condorcet (because the CW beats everybody pairwise, and 
so whenever it becomes the winner so far, it'll stay the winner so far; 
and whenever it's the challenger, it will win against the winner so far 
and become the next winner so far). Furthermore, it's Smith. How cycles 
are broken depends on the agenda.