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

Kristofer Munsterhjelm km_elmet at t-online.de
Thu Jun 18 13:17:11 PDT 2015

```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
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

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.
```