[EM] Current SODA not monotonic; fixable. (mono-voter-raise)

[Jameson Quinn]

2013/4/19 Richard Fobes <ElectionMethods at votefair.org>

> On 4/19/2013 11:09 AM, Jameson Quinn wrote:
>
>> ...
>>
>> So, what do people think? Should I change the default definition of SODA
>> to make it have better compliances? Or should I keep it the way it is
>> because the change would never matter in practical terms and would only
>> make the system sound more complex?
>>
>
> Join the club.  Each of us favors a method that fails some criterion or
> another.
>
> I think the best fix is to identify how often each failed criterion
> occurs.  Probably as a percentage, or a percentage range.
>
> Of course that's difficult to do.  Yet it will be more meaningful than
> just having a yes-or-no checkbox for each criterion.
>
> Keep in mind that if you create a variation of SODA, that amounts to
> creating a new method, which probably requires a new name (or a
> qualification added to the SODA name).
>

OK. I guess this is the best solution. From now on, SODA is the simple
version, and MODA is the monotonic version. MODA has great compliances
(assuming rational candidates), and in order to get them to differ, you
have to fine-tune at least 9-12 different values or orderings (the
preferences, #votes, and #delegated votes for 3 viable candidates and 1
dummy delegator). Assuming that you get the first 2 or 3 for free by
symmetry arguments, that still leaves some small number to at least the 6th
power as the probability of the two systems differing; that is, in
"impartial culture", the probability is at most 1/1,000, and arguably
approaching 1/1,000,000. (OK, "arguably" may not be the right word there,
as it's an empirical mathematical question, so instead of arguing I should
just check it. But that's not easy. Still, I'd bet money that p is 1/50K,
which from an election point of view, is equivalent to 0.)

Aside from my research paper, which is still progressing, I will soon be
publishing a "note" about SODA and MODA on ArXiv, in which I prove MODA's
compliances. Once my research paper, which will reference that "note", is
peer-reviewed, I hope that will be enough to add MODA to
http://en.wikipedia.org/wiki/Voting_system#Compliance_of_selected_systems_.28table.29.
It will join MJ and Ranked Pairs among the overall most-compliant systems
in that table.


> Of course this reply doesn't directly answer your question.
>
> The best solutions are not necessarily easy, but usually they are simple.
>
> Richard Fobes
>
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