[EM] Strategic Bucklin variant?

[Etjon Basha]

Esteemed gentlemen of the EM list,



Among the risks inherent in following some of the discussion here for some
time is that one is apt to start to tinker with rules on their own. Having
done so, one is then apt to present his thinking to the EM list to humbly
ask whether one has reinvented the wheel or, if not, if the method proposed
has any merit.

The idea is to strike some balance between latter-no-harm and favorite
betrayal, perhaps not meeting either but practically meeting both to a good
degree, by mimicking how a reasonable voter would vote given some (but not
full) knowledge of the situation.

The method is a variation of Bucklin where the algorithm used to progress
into the next round is different. Voters present ranked ballots, truncation
and equal ranking allowed. As in Bucklin, majority of first preferences
(but only of first preferences) ends the race. If no candidate has such
majority, the count proceeds in rounds where each ballot reveals N of their
top preferences as follows:

- at any point, the placeholder winner (candidate(s) with most approvals so
far) is revealed

- whoever has not approved of the placeholder winner yet, reveals one more
preference

- whoever has approved of the placeholder winner and no candidate further
below, is stationary

- whoever has approved of the placeholder winner and some candidates
further below, reverts back to revealing only as far down their vote as the
placeholder winner

All “moves” are run concurrently in simulated ignorance of other voters’
moves, all in discrete rounds. When no more moves are possible (all ballots
are either exhausted or go as far down in their preferences as the
placeholder winner) the placeholder winner is elected. The rules change,
mutatis mutandis, where there are two or more placeholder winners at any
given round (reveal only your favorite among them, keep going if you
approve of neither so far).



Has something of the sort (or similar enough) been proposed yet to your
knowledge? If not, would this indeed meet the design criteria of a
compromise between LNH and FB?



Thank you for your time,

Etjon Basha



EXAMPLE 1:

9 voters and 4 candidates, 3 ABC, 2 BDC, 2 CDA

First round: 3 A, 2 B, 2 C. No candidate has majority, count continues, A
in placeholder winner (PW) with 3 approvals.

Second round: 3 A (approves of PW so no more preferences revealed), 2 BD
(reveals one more), 2 CD (reveals one more). D becomes PW with 4 approvals.

Third round: 3 AB (reveals one more), 2 BD and 2 CD (both approve of PW so
no more preferences revealed). B becomes PW with 5 approvals.

Fourth round: 3 AB, 2 B (approves one more than PW, so goes back to
revealing only PW), 2 CDA (reveals one more). A and B become PWs with 5
approvals each.

Fifth round: 3 A (approves one more than their preferred PW, so goes back
to revealing only preferred PW), 2B (no change), 2 CDA (no change). A
becomes PW with 5 approvals.

Sixth round: 3 A, 2 BD (reveals one more), 2 CDA. A still PW with 5
approvals.

Seventh round: 3 A, 2 BDC, 2 CDA. No more moves possible, current
placeholder winner A is elected with 5 approvals.

In this (admittedly convoluted) example A wins but standard Bucklin would
have elected B in round to with 5 approvals, due to A’s votes helping B at
A’s expense.



EXAMPLE 2:

Taken from Warren D. Smith’s February 2014 example of Condorcet
contradiction (https://rangevoting.org/CondCoursera.html)

100 voters, 3 candidates: 35 ABC, 21 BAC, 21 BCA, 21 CAB, 1 ACB, 1 CBA.

Not going through the process, the method elects B in 3 rounds, while the
Condorcet winner is A (incidentally showing this method does not meet
Condorcet). In this case, standard Bucklin would have also elected B.
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