[EM] IRV's Top Preferences Considered First Feature

[Forest Simmons]

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.

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.

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.

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.

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.

Forest