[EM] IRV's Top Preferences Considered First Feature

[Dave Ketchum]

On Thu, 12 Jun 2003 11:33:46 -0700 (PDT) Forest Simmons wrote:

 > A common mantra used in support of IRV is that it considers lower
 > preferences only after the higher preferences are exhausted.
 >
 > One problem with this is that IRV tends to elicit insincere ballots in the
 > most crucial situations (for example, those situations in which plurality
 > is inadequate), so accentuating higher preferences is tantamount to
 > amplifying noise.
 >
 > Another problem with this idea is that a lower preference eliminated at
 > the first stage might have been a higher preference at a later stage had
 > it survived the first cut.  In other words, if your second choice is
 > eliminated at the first stage, then you are stuck with third, fourth, etc.
 > from the second stage onward.
 >
 > The example of several factions with first preferences which are
 > unacceptable (hence truncated) by all of the other factions illustrates
 > this problem:
 >
 > 21 AX
 > 20 BX
 > 19 CX
 > 18 DX
 > 17 EX
 >  5 XE
 >
 > IRV eliminates the "compromise" candidate X at the first stage.
 >
 > Then D, C, B, and A are successively eliminated at stages when their
 > supporters would wish that X were still in the running, since X would be a
 > higher choice than any of the remaining ones.
 >
 > IRV gives the win to E in the final show down of E beats A, 22 to 21.
 >
 > Is E really better than A ?  If so, then only by virtue of a "lower
 > preference" of the five X supporters.  If not, then the plurality winner A
 > is better than the IRV winner.

The above is also what Condorcet backers say of IRV.  Condorcet would see
that all the voters find X acceptable, and more acceptable than any other
candidate.
 >
 > Here's another way of putting the "top preferences count most" feature of
 > IRV into perspective:
 >
 > Approval runoff would degenerate into IRV if every voter were constrained
 > to approve only one candidate at each stage of the runoff.

I am not sure exactly what "Approval runoff" is, except here it seems to
involve getting voter involvement at each stage, after previous stage
votes have been counted.  I see this as unacceptable for public elections,
especially for such as mayor or governor, unless it offers some TREMENDOUS
advantage.  Here the first stage would be voted by each voter during
election day.  The next stage would have to be at some later date.
 >
 > That would be tantamount to constraining all of the preferences to fit the
 > pattern  A>>>B>>C>D,  reflecting successively smaller utility gaps as we
 > move from the higher ranks to the lower ranks.
 >
 > [i.e. if voter utilities did fit this pattern, then in a zero information
 > approval runoff, their best strategy would be to approve only their
 > highest remaining choice at each stage of the runoff.]
 >
 > Approval runoff would degenerate into Coombs if every voter were
 > constrained to approve all candidates but one at each stage of the runoff.

There can be a dozen candidates - I expect more than with Plurality with
any method, such as Condorcet, that lets candidates know better how well
they are liked.  Unacceptable to me to demand marking 11 candidates, but
could mark the one least liked.
 >
 > That would be tantamount to constraining all of the preferences to fit the
 > pattern  A>B>>C>>>D, which would be appropriate only if the utility gaps
 > tended to be larger at the lower end of the preferences.
 >
 > Why would you want to artificially constrain the voter ballots in an
 > approval runoff in a way that would not reflect voter utilities except by
 > extremely rare coincidence?
 >
 > Indeed artificial ballot constraints tend to elicit insincere ballots.

I do not see Plurality's constraint of approving only one candidate as
artificial but, anyway:

Approval removes Plurality's constraint, but adds one of its own - which
looks more artificial to me - I can approve of more than one candidate,
but am not permitted to indicate which approved candidates I like best -
something I VERY OFTEN would desire to do once I can vote for more than one.

Something I would like in Condorcet, but have not read of its being there,
is being allowed to indicate my liking for two or more candidates is tied
- thus removing one more constraint.  Adapting the count is not difficult
- we normally count 1 for the one the voter prefers in each pair - simply
count 0.5 for each member of a pair when the voter indicates a tie between
them.
 >
 > The unconstrained version of approval runoff is barely harder than the
 > artificially constrained versions, just as approval is barely harder than
 > plurality.
 >
 > In fact, removing the one mark per row constraint from the standard IRV
 > ballot for ranking N candidates, converts it into a (dyadic) Cardinal
 > Ratings ballot with resolution 2^N, which is perfectly adequate for
 > approval runoff for N candidates.
 >
 > Like IRV this version of approval runoff is summable in data structures of
 > size 2^N, so IRV offers no significant advantage over approval runoff that
 > would offset its gross disadvantages.

This 2^N rapidly becomes enormous - much more space and much less
readability than Condorcet's N^2 when you get past 4 candidates.
 >
 > Forest
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    Dave Ketchum    108 Halstead Ave, Owego, NY  13827-1708    607-687-5026
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