[EM] SODA arguments

Jameson Quinn jameson.quinn at gmail.com
Sat Feb 18 05:29:24 PST 2012

>  It seems to me that there would be a lot more candidates under SODA.
>> It's pretty hard to spoil the race and there is benefit to
>> be had in receiving some votes. It seems parliamentary that way. How many
>> supporters is too few to consider running?
>> Well, there is the 5% cutoff, below which your votes are automatically
>> assigned for you.
>> That's not really a punishment though. The candidate will probably get
>> what they would've done anyway.
>> I really think this is an issue that might need a rule of some kind. Why
>> nominate one when you can nominate five? Anybody
>> who appeals to some segment of the electorate could help bring in votes.
>> Can you imagine if, for example, the Republicans
>> were able to nominate every single one of their hopefuls for the
>> presidency, with the knowledge that in the end all their votes
>> would probably pool together? You don't have to like Gingrich, you can
>> vote for Cain. And maybe your vote will end up
>> with Gingrich, but without Cain you might not have cast it at all.
> That's a fair point....

I've thought some more about the "just nominate everyone" problem, and I
think it may be worth making a SODA rule to deal with it. The problem with
the "first > second + third" rule is that it primarily focuses on the big
candidates, while the marginal choice of whether to throw one more hat in
the ring is made by the small candidates. So why not do something more
obvious: if a candidate gets less than 1%, they cannot use their delegated
votes at all.

Say candidates are naturally distributed by a modified form of Zipf's law,
with the top two candidates set to equal. That is to say, the top two
candidates have X% support; the next one has half that, X/2; the next, X/3;

It would take 21 candidates to get down to 1% support, and if all votes
were delegated or bullet votes, the top two would have 22% support each.
The minimum majority coalition would be 7 candidates.

If voters were a little more wary of wasting their vote, and left a safety
factor of 2 (that is, refused to vote for a candidate whose support was
under 2%), then there would be 12 candidates, and the top two would have
24% support each, and the minimum majority coalition would be 5 candidates.

And if voters had a safety factor of 2, but there were a 1/3 chance of
adding one more approval (that is, 2/9 of voters vote for 2 candidates,
2/27 vote for three, etc.; a total of 150% approvals) then there would be
14 candidates, the top two would have 35% support, and the minimum majority
coalition (using only the delegated, not the approval, votes of all but the
first coalition member) would be 3 candidates.

Of course, if you use a reasonable power law instead of Zipf's law, the
number of candidates would tend to be less, although the minimum majority
coalition might be slightly larger.

These numbers sound reasonable to me. I think the 1% cutoff would be a good
rule, and I'm considering adding it to the definition of the standard
version of SODA. What do others think?

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