[EM] STV when applied to choosing pizza toppings

[James Gilmour]

> Nathan Larson asked:
> 
> Does anyone have any comments in reference to this critique 
> of STV as applied to choosing three pizza toppings? The issue 
> is whether it's fair to transfer the surplus votes from the 
> winners before transferring votes from the losers. 
> 

The person who wrote the comments you quoted (below) does not understand
the origins of STV-PR or understand how it is generally intended to
work.  Instead, the writer shows a classical social choice approach to
interpreting the information on the ballot papers.  But the preferences
marked on an STV-PR ballot paper should not be interpreted in that way.
Instead, they should be seen for what they are, contingency choices, to
be brought into play ONLY in the event that the voter cannot be
represented by his or her first choice candidate.  STV-PR was not
devised in an attempt to identify some great community-wide consensus
(maximising some imputed social utility).  Rather, STV-PR was devised to
ensure that each significant point of view within the electorate was
represented fairly (as expressed by the voters' responses to the
candidates who had offered themselves for election).  Originally, the
intent was to maximise the diversity of representation rather than
maximise the consensus of representation, but there has been some de
facto shift in that by changes made to the counting rules (for the
extremes, compare Dáil Éireann STV rules with Meek STV rules)..

One of the undertakings normally given to voters in any STV-PR election
is: "under no circumstances can a later preference harm an earlier
preference".  This is completely consistency with the 'contingency
choice' approach to marking preferences.  Any other approach would
discourage voters from marking all the preferences they really have or,
worse, open the door to tactical voting on a large scale.

Seen from this perspective, it will be clear that it is essential to
transfer any surplus before you consider the exclusion of the
candidate(s) with fewest votes.  Where the surplus is so small that it
could not change the order of the bottom candidates, some STV counting
rules provide for the transfer to be held in abeyance, but that doesn't
alter the general principle.

James Gilmour




> ---
> What you describe would indeed work, however....
> 
> Suppose the second choices of the 100 "winner" (pepperoni) votes were
> one half for mushrooms, one half for onions. This, if I follow the
> numbers correctly, means that mushrooms and onions would win (with 40
> and 56 respectively). But look: you have completely ignored the second
> (and third) choices of the folks who didn't vote for pepperoni as
first
> place. You just disenfranchised 56 voters. Why should only the
> pepperoni-first voters be the ones who get to exercise their second
and
> (possibly) third choices? Doesn't seem fair to me! Those 56 NAP
> members who didn't vote pepperoni first may ALL have voted (yuk)
> anchovies as their second choice. Clearly that would exceed the quota
> and anchovies would have garnered MORE votes that any of the
> non-pepperoni choices. But you trashed them. For shame!
> 
> With smaller numbers the problems become more apparent. I am taking
the
> liberty of e-mailing you directly the essay I did some years ago.
> Enjoy! Meanwhile I'll think about constructing a counter example where
> there is no choice but an arbitrary choice (following your rules) that
> causes a different outcome.
> 
> But not tonight. Too late.
> 
> 
> John
> 
> John D. Stackpole, CPP, PRP Voice: 301.292.9479
> Parliamentary Services Fax: 301.292.9527
> 11 Battersea Ln. jstackpo at ...
> Ft. Washington, MD 20744-7203