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Why the default option is special



[There's an irony here which is probably worth noting.  In past
discussions, Anthony Towns had been in favor of eliminating all options
which don't beat the default option early on in vote resolution, rather
than including any special treatment of the default option in any
iterative part of the vote resolution process.  And, I had been opposed.]

Background:  http://electionmethods.org/Arrow.html

Arrow defined a set of criteria which an ideal voting system should have,
and then proved that no voting system could satisfy all these criteria.
A part of his model is that only the winner of the vote is relevant.

The tough votes to decide are those where cyclic ambiguity exists.
[For the current proposed ammendment: those where the schwartz set
contains more than one member.]

There's two ways of resolving cyclic ambiguities:

[1] Use some mechanism to pick from among the ambiguous choices
[2} Discuss further and vote again

When the majority of voters agree that something should be done, it's
pretty clear that [1] is better than [2].

When the majority of voters do not agree that something should be done
it's pretty clear that [2] is better than [1].

The default option is our mechanism for distinguishing between these
two cases.

Note that the default option cannot be cloned: options which rank below
the default option are "bad options", options which rank above the default
option are "good options".  Thus, we SHOULD ignore voting criteria which
expect to treat the default option as if it were any other option.

Thus, to some degree, any of the options which beat the default option
are acceptable options while none of the options which are beaten by
the default option are acceptable options.

Finally, here are the vote tallies for our past non-leader votes.
In essence, this shows that the default option has not been a popular
option, and (more generally) that the proposed changes to the voting
system would not have affected the outcome of any of these votes.

To read these tables: rows represent votes for an option, columns
represent votes against an option.  Thus, if you see a 5 if the second
row and the third column that means that there were 5 ballots which
explicitly preferred the second option to the third option.

constitution
 0 86 86                "y - Yes"       / winner
 0  0  5                "n - No"
 0 58  0                "f - Further discussion"

logo1
  0 37 77               "s - SINGLE License"
 69  0 85               "d - DUEL Licnese"      / winner
 20 17  0               "f - Further Discussion"

logo2
   0 15  37 22 18 24 22  39             "a - ANTS"
 103  0 104 89 92 77 84 104             "w - SWIRL"     / winner
  35 16   0 22 20 17 24  38             "e - SEAL"
  88 47  85  0 69 54 64  86             "o - OLD"
  72 36  73 46  0 43 48  78             "c - FIXED CHICKEN"
  87 57  91 69 74  0 65  90             "d - DG"
  67 36  67 58 54 54  0  72             "m - MODIFIED"
  56 27  61 32 33 32 38   0             "f - FURTHER Discusson"

logo3
  0 89 96               "s - FOR logo swap" / winner
 20  0 38               "a - AGAINST logo swap"
  9 44  0               "d - FURTHER Discussion"

[The constitutional vote is the only one that would reasonably have a
supermajority requirement.  Here, the winner was unanimously preferred
over all alternatives.]

Looking at the logo votes:

vote            winner beat     winner beat
                status quo by   next most preferred option by
logo1           4.25:1          1.86:1
logo2           3.85:1          1.35:1
logo3           10.7:1          4.45:1

Here, all of the non-default options were classified as significantly
better options than the default option.

FYI,

-- 
Raul



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