There was one point that I tryed to make in my initial post about
unusual behaviour of supermajorities and quorums, that Andrew Pimlott
summed up more nicely than I did.
Andrew Pimlott wrote:
> Any method in which an option can be eliminated "early"--ie, without
> a fully head-to-head with all the other options--has the same
> fundamental flaw as instant runoff, and should be rejected for the
> same reason.
> So for example, the clause, in most drafts, that first eliminated
> options that were defeated by the default option, was a direct
> invitation to insincere strategic voting. It would encourage voters
> to put the default option second, in an attempt to knock out the
> other candidates early. Exactly what we're trying to avoid with the
> Condorcet method.
With that clear explaination, and my somewhat vague examples in my post,
the "default option" thats drops defeats early seems to encourage
strategy, and should not be used.
When I made my previous proposal, I incorrectly assumed that all
non-default options would have identical supermajority and quorum
requirements, which Raul Miller almost immediately pointed out as
incorrect, and shortly following Anthony Towns illustrated a practical
example of having non-default options without supermajority requirements.
With this proposal, I've tryed to achieve two main goals, which have
seem to eluded previous drafts at least as far as I can tell, and in
particular my own attempts.
(i) Supporters of options that require supermajorities can not use the
strategy of introducing a weak non-supermajority candidate to the
benefit of their supermajority restricted candidate. (Reduce Strategy)
(ii) Re-running an election with the new winner and default with
identical votes produces identical results. (Consistency)
Both of these properties seem to be closely related to the
implimentation of the default option, so I've toned down its effects, in
particular this implimentation does no early defeats.
In the process of trying to achieve the above two goals, its likely I've
broken other things, but its worth a try.
In any case, I have a vague feeling that maybe this might actually work
- Definition: Defeat is the normal defeat, not considering supermajority
and quorum requirements.
- Definition: A super-defeat is a defeat after considering supermajority
and quorum requirements.
(a) The default option is considered.
(i) If option A has quorum requirements and supermajority requirements
less than or equal to option B, and option A defeats option B, then
option A is considered.
(ii) If option A super-defeats all options with quorum requirements or
supermajority requirements less than option A, then option A is considered.
Perform CSSD on all considered options, ignoring supermajority and
(Keep a close eye on the or's and and's in the rules in part (b))
To illustrate the properties of this method, I'll use an example.
For simplicities sake, assume we have two sets of options, one requiring
supermajorities (the non-default group), and the other which doesn't
(the default group).
The default option is a member of the default group.
Rule (i) immediately makes sure all members of the smith set of the
default group are considered, at least.
For members of the non-default group, these members can not use rule (i)
to be considered, as members of the non-default group do not have quorum
and supermajority restrictions less than or equal to the only currently
considered options in the default group.
So they must use rule (ii) to be considered. This means they have to
super-defeat, that is, over their supermajorities, all options which
have super-majority or quorum requirements less than themselves. That
is, for a option in the non-default group to be considered, it must beat
all options in the default group. This removes the strategy of adding
weak options to the default group, as all options in the default group
have to be defeated anyway. [Reduce strategy]
However, after one option of the non-default group is considered, other
members of the non-default group can begin to be considered also, just
by defeating that considered non-default group option using rule (i).
This prevents identical elections from producing different results, and
if a supermajority is achieved, it is awarded to the most prefered
option first time, instead of after a re-election with identical votes.
Also, the ignoring of supermajorities and quorums in the final
resolution of considered options (c) further improves consistency due to
identical propositions between options in elections with identical votes.
Anyway, hope you all enjoy finding an example to break this proposal
into little pieces, and then maybe even salvage it and improve it.