[EM] The 'post mortem' discussions on UK radio (from Steve)

[Kristofer Munsterhjelm]

On 06/18/2015 05:49 PM, steve bosworth wrote:

> Because you want both a 'simple' and 'fair' electoral system, perhaps
> you would like to consider APR. It is referred to in my next comment to
> James Gilmour. APR's countrywide count with its modified STV would be
> administured through all the single member constituencies that remained
> after APR's primary election. Consequently, rather than having to rank
> more than one candidate, each citizen would still have the option of
> voting only for one candidate, much as they do now using FPTP. At the
> same time, each such vote would still be guaranteed to continue
> mathematically to count in the legislative assembly. APR seems to offer
> your 'fairness throughout'. APR is almost as simple as party-list
> systems but puts each citizen in control of to which representative's
> 'weighted vote' her vote will be added.
>
> What do you think?

Unfortunately, because APR reduces to IRV, I can only consider it 
asymptotically fair (that is, when you have enough seats compared to the 
number of candidates). I would much rather have an APR-like method based 
on one of my Bucklin methods for the actual count, because neither 
Bucklin/MJ nor Range exhibit monotonicity failures.

Perhaps you would accept a Bucklin variant of APR as well, though I 
would have to write up the algorithm in a more user-friendly way than I 
have in my past posts. The basic idea is that instead of eliminating 
candidates, you set a support threshold so that a candidate is elected 
after achieving that support, and then you gradually add inn first 
preferences, second preferences, etc. When a candidate exceeds the 
threshold, all the voters whose votes contributed to the candidate's 
election are associated to that candidate, and then the count continues 
without them.

You then try different thresholds until you find one where only the 
number of candidates you want to be is elected (say, a single winner or 
three winners), and then each winner is given a weight corresponding to 
the number of voters associated to that winner.

Just like IRV APR, every voter's vote matters in the sense that it 
increases the weight of a winner; and there are (to my knowledge) no 
monotonicity problems of the sort where ranking X higher might lead to X 
being defeated. Furthermore, it handles certain scenarios with 
compromise candidates better than IRV, and can be used for both ranked 
votes and rated ones[1].

If the IRV method's intuition is of a sequential elimination 
competition, Bucklin is one of repeated voting until the voters reach an 
agreement. The voters start off being very picky about what candidates 
they want to give their votes to (corresponding to a high threshold), 
then they become less and less picky and try again until there are 
enough winners. In practice, the algorithm would use a binary search 
instead, but the outcome is the same.

Neither Bucklin nor IRV would be as good as say, using a weighted 
variant of Monroe's method or Statistical Condorcet (if it can be 
simplified). But either of these would be a lot more complex.

I would also have to check if the other concepts of APR are reasonable. 
I haven't been investigating it much as I have been busy with other 
things. What I am saying is that reducing to IRV makes it too sketchy 
for me unless it's used with a lot of winners relative to candidates. If 
simplicity is number one, I'd rather have your Asset fix be the default 
mode of operation[2].

[1] There's also a distant connection to party list PR systems. 
Webster's method can be phrased as: if party (or state) p has v_p votes 
(or population), find x so that (sum over all p: round(v_p * x)) equals 
the number of seats you want. Again you find a threshold that gives the 
right number of winners.

[2]  Or emulate the Bucklin intuition in the town hall setting by 
letting the voters remove and add their vote whenever they feel like it, 
and stopping the process when only three (or seven, or however many) 
candidates have nonzero support and none have greater than 20% support 
(or what your threshold was). The voters will start off being picky and, 
seeing that that doesn't get them nowhere, will gradually become more 
lenient. However, it will be messy and may not follow Bucklin well since 
there are no restarts. In a town hall setting, regular majority vote or 
parliamentary procedure might be good enough in any case, because there 
are relatively few voters.