[EM] Choosing leaders in a legislature

[Andy Jennings]

Jameson,

Your solution to the original problem (use an anonymous voting system) is
not a bad one, but it is still interesting to consider the problem where
the voting system is not anonymous and going against your caucus is indeed
punishable behavior.  Suppose the caucus loyalty is so strong that the
entire majority party votes as a bloc.  What voting systems will still
elect some kind of compromise candidate?

With all of our top-tier methods (Range, Approval, MJ, Condorcet), there is
a defined way for a majority bloc to vote that will ensure their outcome no
matter how the minority votes.  IRV too.

Interestingly enough, Borda Count can give us a compromise winner in this
situation, if the majority votes first and the minority can see the totals
and vote reactively.  The majority can't put enough distance between their
chosen winner and the other candidates to knock them all out of the
running.  In effect, they must leave N candidates within striking distance
and then, if the minority unites, they can elect any one of those
candidates.  I haven't had the time to calculate N.  It depends on the size
of the majority and the minority as well as how many candidates there are.
 My thinking was that if that's how the game theory works out (majority
nominates N candidates and the minority chooses between them) then why not
just make that process explicit?  Tell the majority to nominate N
candidates and then let the minority choose between them.  Then we can
choose the number N directly, we're not limited to the one that falls out
of the Borda construction.

This method can still choose the median leader without instituting
anonymity or challenging caucus loyalty.  I'm just not sure, yet, how it
extends to more than two parties.

~ Andy


On Mon, Nov 12, 2012 at 1:32 PM, Andy Jennings
<elections at jenningsstory.com>wrote:

> Good thoughts, Jameson.
>
> I think you are right that if voting was anonymous and a good voting
> system were used, it would turn out pretty well.  Also, it is necessary
> that *running* for leadership not be a punishable offense.  The easiest way
> to fix this, I think, is to say that every legislator is in the running for
> leadership and you can't opt out.  Would those two structural changes be
> enough, then?
>
> More thinking about the original proposal:
>
> What if both parties, in their caucus and using whatever voting system
> they wanted, nominated 16 legislators for leader.  Then there will be at
> least one legislator approved by both parties.  (If there is more than one,
> then hold approval voting runoffs in the whole legislature, or something.)
>  This is pretty close to my earlier proposals, and I don't think the
> incentive to nominate turkeys would be all that great.
>
> If there were three parties, you could have each party nominate 21 people
> so there is at least one legislator approved by all three parties.   This
> is equivalent to allowing each party to eliminate 10 people.  You do these
> eliminations sequentially, largest party to smallest party, or the reverse.
>  Or you could let each party eliminate one at a time, in ten rounds, until
> there was only one left.  But any of these options seems to give a big
> advantage for a party with just under a minority to split into two parties.
>
>
> On Mon, Nov 12, 2012 at 5:33 AM, Jameson Quinn <jameson.quinn at gmail.com>wrote:
>
>> Why not just use approval voting (or MJ) within the legislature? The
>> problem with the "nominate 16 and we'll pick one" idea (and the like) is
>> that it gives a strong incentive to nominate candidates that, for whatever
>> reason, everyone knows are unsuitable.
>>
>> To me, the basic way that the approval voting could go wrong is if voting
>> outside your caucus were a punishable betrayal. So, I think you'd need to
>> have a secret ballot. That's unfortunate for ordinary voters, who generally
>> should have the right to know what their representatives are doing in their
>> name. But other than that, I think that the incentives are pretty good, and
>> it would settle on a capable near-median candidate.
>>
>> Jameson
>>
>> 2012/11/11 Andy Jennings <elections at jenningsstory.com>
>>
>>>  What would be the ideal way to choose leaders in a legislature?
>>>
>>> In the Arizona house and senate, for example, once our legislators are
>>> elected, the majority party caucuses to choose the leadership.  Assuming
>>> the Hotelling model, let's say they end up choosing the median legislator
>>> on their half of the political spectrum.  It follows that the legislature
>>> will be led by someone from about the 25th percentile on the political
>>> spectrum.  Then, if the other party gains control, the leadership will
>>> swing to the 75th percentile on the political spectrum.  Wouldn't it be
>>> much better we could force the leadership to be near the median of elected
>>> legislators?
>>>
>>> In the Arizona senate, for example, which has thirty members, the
>>> majority party may have as few as seventeen members and the caucus could be
>>> controlled by nine, or thirty percent of the senate.  I'm not sure, but I
>>> have to imagine that this is common.
>>>
>>> Here are some ways to force the leadership near the median (assume a
>>> legislative body of 31 members and just two parties, for now):
>>>
>>> 1. "The majority party shall nominate 16 senators for president and the
>>> minority party shall choose among them."
>>>
>>> 2. "The minority party shall nominate 16 senators for president and the
>>> majority party shall choose among them."
>>>
>>> I think either of those would tend to choose a president near the
>>> median.  Is one better than the other?  Is it possible to extend to
>>> multiple parties?  Without forcing them to form a majority coalition first?
>>>
>>> Say there are three parties.  Should each party, in turn, eliminate ten
>>> people?  Does the largest party or the smallest go first?
>>>
>>> Or should the first party eliminate 15 and then the other parties choose
>>> among the remaining 16 via approval voting or something?
>>>
>>> Other ideas?
>>>
>>> ~ Andy
>>>
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>>>
>>>
>>
>
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