[EM] In defense of the Electoral College (was Re: Making a Bad Thing Worse)

[Kristofer Munsterhjelm]

Dave Ketchum wrote:
> On Fri, 07 Nov 2008 09:58:30 +0100 Kristofer Munsterhjelm wrote:

>> I think an NPV-style gradual change would have a greater chance of 
>> succeeding than would a constitutional amendment. The constitutional 
>> amendment requires a supermajority, and would thus be blocked by the 
>> very same small states that benefit from the current Electoral College.
> 
> An NPV style change MIGHT have a greater chance than an amendment but:
>      It would be incomplete.
>      Small states could resist for the same reason.

If the small states resist, the large and middle sized states will 
attain a majority, and thus through the compact/agreement overrule the 
others. At that point, it'll be in the interest of the small states to 
join since their share of power by staying outside the system is 
effectively zero.

> Note that small states could retain their advantage with an amendment -- 
> as I proposed.  What might all states compromise on?

That would depend on the nature of the agreement. Either it would be 
straight NPV (all states weighted by population) or it would be 
according to current (EC) weighting.

For an amendment, it's possible that small states would oppose the 
amendment if it's population-normalized, whereas large states would 
oppose it if it was electoral-college-normalized.

>> As for the system of such a compact, we've discussed that earlier. I 
>> think the idea of basing it on a Condorcet matrix would be a good one. 
>> That is, states produce their own Condorcet matrices, and then these 
>> are weighted and added together to produce a national Condorcet 
>> matrix, which is run through an agreed-upon Condorcet method.
> 
> How do we tolerate either weight or not weight without formal agreement 
> (amendment)?

I imagine a clause like: "The maximum power of a state shall be its 
population, as a fraction of the population of all states within the 
compact. Call this power p. The state shall be free to pick an x so that 
the weighting for this state is p * x, 0 <= x <= 1". That's for the 
closest thing to NPV. For a continuous electoral college, the first 
sentence would be "The maximum power of a state shall be the sum of its 
number of representatives and senators, divided by the sum of the number 
of representatives and senators for all states within the compact". 
There's no reason to have x < 1 but for future agreements to mutually 
diminish power (to turn an EC compact into a population-normalized one 
or vice versa).

I'll add that this phrasing would give states the same power no matter 
the relative turnout. If that's not desired, it could be rephrased 
differently, but giving states the same power is closer to the current 
state of things. The continuous electoral college variant does not take 
into account the 23rd Amendment, either.

>> If all states use Plurality, well, the results are as in Plurality. If 
>> some use Condorcet, those have an advantage, and if some want to use 
>> cardinal weighted pairwise, they can do so. Yet it's technically 
>> possible to use any method that produces a social ordering (by 
>> submitting, if there are n voters and the social ordering is A>B>C, 
>> the Condorcet matrix corresponding to "n: A>B>C"). While imperfect, 
>> and possibly worse than Plurality-to-Condorcet or simple Condorcet 
>> matrix addition, the option would be there, and would be better than 
>> nothing.
> 
> Actually each state does only the first step of Condorcet - the NxN array:
>      If a state does Condorcet, that is exact.
>      If a state does Plurality, conversion as if voters did bullet 
> voting in Condorcet is exact.
>      If a state does something else, it has to be their responsibility 
> to produce the NxN array.

Yes. What I'm saying is that it's theoretically possible to incorporate 
any voting method into this; however, the results might be suboptimal if 
you try to aggregate, say, IRV results this way, since you'd get both 
the disadvantages of IRV and Condorcet (nonmonotonicity for the former 
and LNH* failure for the latter, for instance).

> States have differing collections of candidates:
>      In theory, could demand there be a single national list.  More 
> practical to permit present nomination process, in case states desire such.
>      Thus states should be required to prepare their NxN arrays in a 
> manner that permits exact merging with other NxN arrays, without having 
> to know what candidates may be in the other arrays.

The easiest way to do this is probably to have the candidates sorted (by 
name or some other property, doesn't really matter). When two matrices 
with different entries are joined, expand the result matrix as 
appropriate. Since the candidate indices are sorted, there'll be no 
ambiguity when joining (unless two candidates have the same names, but 
that's unlikely).