[EM] In defence of IRV

Kristofer Munsterhjelm km_elmet at t-online.de
Thu Nov 18 06:02:52 PST 2021

```On 16.11.2021 13:22, Richard Lung wrote:
> To all, re KM on STV,
>
> Small districts are in no way integral to STV. Clarence Hoag and
> George Hallett introduced at large districts to US cities.  New York was
> at-large STV. That's why it could boast a communist or two, whose main
> purpose was to uphold the rights of marginalised labor. Hallett made the
> point that you didn't need primaries with STV because STV secured them
> (in an at large election).
> Cambridge still has an at-large STV 9 member constituency.
>
> The introducing of more than one voting method in any election is a
> bad idea, because science aspires to one truth, not two. But MMP already
> is two contradictory methods, both wrong. And two wrongs don't make a right.

I don't think that follows.

To use a Norwegian example: Currently we use what is essentially party
list with top-up seats (called "levelling seats"). How this works is
that first the county (district) seats are allocated according to the
support in each county[1] using modified Sainte-Laguë, then the top-up
seats (one per county) is allocated, using a separate greedy algorithm,
to increase nationwide proportionality among the parties who pass the
threshold.

So this is two voting methods and two wrongs, right?

But now consider an alternative approach: you set up a matrix where each
row gives the support (in number of votes) for a given party in the
different countries, and each column gives the support for the different
parties in a county. Let the element corresponding to the support of
party p in county c be v_c,p.

Then there exists an algorithm that determines county and party divisors
(d_c, d_p) so that when the number of seats party p gets in county c is
round(v_c,p/(d_c * d_p)), the sum over all parties for a given county
equals the number of seats apportioned to that county; and the sum over
a given party for all counties is equal to the number of seats that
party would obtain if there was only one district.

This is the Pukelsheim method, biproportional apportionment. And it's
one procedure. Yet the outcome is much the same: local proportionality
is reduced so that national proportionality can be increased.

There are many reasons to favor the second over the first - for
instance, the greedy algorithm can get stuck in a local optimum that
seems obviously wrong. However, that one makes use of two procedures and
the other makes use of only one doesn't seem, to me, to be one of them.

They both aim to achieve the same objective; whether that objective is
desirable should, IMHO, be considered separately from what method might
be used to achieve it. And given some objective to be achieved, the
methods should be judged by how well they accomplish the task (and at
the cost of what kind of undesired behavior), rather than by the
particular construction of their algorithms.

-km

[1] Currently only some of the district constituencies match up with
county borders due to the last government's county reform. The current
government intends to revert some of these changes.
```