STV (was Re: ternary operator vote)

[Alex Martelli]

On Wednesday 12 February 2003 12:47 pm, Laura Creighton wrote:
> clarification:
>
> are you proposing that we rank our candidates, once, and produce one
> ballot which gets ground through the election process again and again,
> or are you suggesting that we eliminate one candidate, and then
> hold the vote again with people getting to reorder if they like?

The "S" in "STV" stands for "Single" (I think in a single-winner context
it's also called "alternative voting").  As far as I know it's used in 
Ireland, Northern Ireland when allowed (for European Parliament,
NI Assembly, local elections), Australia, Malta -- mostly in multiwinner
contexts that make things a bit more complicated, but anyway.

In other words, I propose each voter mails in a list of candidates in
his or her order of preference, e.g.:

   A B G F E C H D 

the voter does not have to rank ALL candidates -- not even ranking
a candidate means "if all that's left are candidates among those I
didn't rank, then I abstain".

There are no advantages to letting the voter reshuffle the list over
and over.  The above example means: "I prefer A; if that is not an
option, I second-prefer B; if A and B are not options, I third-prefer
G" and so on.  Say that A receives the least number of votes so
it drops out: very well, the voter has ALREADY said what he or
she wants in such an eventuality -- no reason to reorder.


One possible anomaly is, e.g.:

45% of voters prefer A, C
35% prefer B, C
20% prefer C, B

i.e., C has few enthusiasts but as a least of evils it's somewhat
acceptable to everybody -- A enthusiasts who loathe B _and_
B enthusiasts who loathe A.

_However_ with STV, C would drop out first, having the least
number of first-preferences; this would raise B to 55% and B
would get chosen.

Suppose social utility is the sum of individual utilities and every
individual voter's utility is x if his or her first choice gets in, y
if the second choice, 0 if the third/abstained-on choice.

Then electing A would give social utility of 45 x;
electing B, 35 x + 20 y;
electing C, 20 x + 80 y.

For B's election to be optimal needs:
    35 x + 20 y > 45 x               i.e. y > 0.5 x
    35 x + 20 y > 20 x + 80 y     i.e. y < 0.25 x
in other words, B's election can never be socially optimal under
the given hypotheses.  A's election would be optimal if
    45 x > 20 x + 80 y               i.e. y < 5/16 x
otherwise, C's.  Clearly this is purely indicative given the many 
simplifying hypotheses (additive utility, equal utility ratios for
all voters between first/second/third choice...), still it does
indicate a potential problem.


Funny that I'd never thought of that when thinking of STV
in the abstract but thinking of it in terms of pep 308 voting
brought it to mind in a hour or two;-).

Anyway, I think the risk of such anomalies is minor, and the
idea of having each voter indicate a quantitative measure
of his or her utility per choice *IS* getting too complicated
IMHO.

Given the purely consultative nature of this vote, I think STV
is in any case quite appropriate -- the BDFL can be presented
with the vote's result not just in terms of "preferred alternative
is X", but in a more articulated way -- WITH notes about the
number of voters for which the various alternatives were first,
second, and third choices, for example -- so he can make up
his mind on the basis of more info on voters' preferences.

But I accept it's a matter of opinion, since anomalies CAN
exist (although, I keep claiming, more rarely than they can
with other voting systems --  but, this IS arguable;-).  You will
find many pro-STV sites on the net, and a few pointing to
problems with several variations of it.


Alex