[EM] Sequential Proportional Approval - A Better Proportional Representation Electoral Method (was: SAV)

[Jameson Quinn]

2010/5/21 Abd ul-Rahman Lomax <abd at lomaxdesign.com>

> At 02:05 PM 5/20/2010, Jameson Quinn wrote:
>
>> I was talking about SPA, not SAV. SPA (summable proportional approval) is
>> a summable method which, with very high probability, corresponds to
>> Sequential Proportional Approval, first proposed by Thiele (c.1890). This in
>> turn corresponds, with high probability, to the following simple procedure,
>> which I think is easy enough for anybody to understand:
>>
>> 1. Collect approval ballots
>> 2. Count the ballots and elect the approval winner
>> 3. Select a droop quota of ballots which approve the approval winner and
>> discard them. First discard ballots which only approve already-elected
>> candidates; then randomly select the rest. If there are not enough ballots,
>> discard all available.
>> 4. If the council is not full, repeat from step 2.
>>
>
> Yeah, and to avoid the random selection problem, which could wreak havoc
> with auditing, you'd keep all the ballots and just devalue them
> proportionally to give them the proper remaining vote strength. I.e., if
> there are N ballots, with quota Q, the ballots would now be worth (N-Q)/N,
> but not less than zero.
>

Yes. That is the actual system in Sequential Proportional Approval. As I
said, the process above only "corresponds with high probability". I said the
above to be simpler.

In fact, the statute could actually just say "the most probable result with
[the process above]". That would be 100% equivalent to the fractional vote
process, without having to try to translate the whole reweighting process
from mathematics into lawyerese (which is always ugly).

>
> That's more complicated, to be sure, it requires maintaining sets of
> devalued ballots. This could be done centrally, in fact, by categorizing
> ballots into vote combinations, but that's also a lot of data to transmit.
> Ultimately, with computers for analysis, and public ballot data -- another
> reform I'm very interested in -- the analysis could be done easily.
>

And that's where the brilliance of the summable method comes in. It's
something you wouldn't dream of doing without a computer; but the data to
input to the computer is something that can easily be published in the
newspaper, a matter of one NxN square and one NxN triangle, with 2N
dimensions of redundancy.

And for simplicity, *the summable method is not the official count, but it
is the official grounds for a recount*. The statute says: "the official
result is the most likely result for [the process described above],
calculated using fractional votes. The summed results (correlation matrix
and number-of-approvals-versus-candidates matrix) are published ASAP, and if
2 of the 3 biggest local math departments determine that those summed
ballots are within N votes of indicating a different result than the
official results, then you have a recount." Obviously when the summable
results are published before the official centralized count, anybody (or any
newspaper) with the algorithm can calculate the almost-certain "provisional
winners". That way, you get all of the verifiability and speed advantages of
summability, but none of the statutory complexity.

Kathy, what do you think of that?

JQ
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