[Election-Methods] RE : IRV variant (was 'Median or "ladder" voting with candidates')

[Chris Benham]

Kevin,
Both of our suggested IRV-like methods lose both of
regular IRV's compliance with Later-no-Harm and
Later-no-Help.

48:A(>B>C)
03:B>A>C
49:C>B>A

In your Instant VFA Runoff (IVFAR) A wins if the 48A
voters truncate, but if they vote A>B>C then C is
eliminated and B wins.

46:A
03:A>B
25:B>C
27:C(>B)

In my suggested version if the 27C voters truncate
then
both A and B are eligible to be eliminated so B with
the fewer top preferences is eliminated and C wins,
but if they vote C>B then only A can be eliminated in
the first round and then B wins.

46:A
03:A>B
25:B(>C)
27:C>B

Here in IVFAR if the 25B voters truncate then nothing
prevents B from being eliminated in the first round,
but if they vote B>C then A is ranked strictly bottom
on more than half the ballots so is eliminated and B
wins.

48:A(>C)
03:B>A
49:C>B

In my version if the 48A voters truncate then only C
is eligible to be eliminated so C wins, but if they
vote A>C then B is eliminated and A wins.

So my suggestion swaps the two LNHs for Minimal
Defense while IVFAR loses the LNHs and Irrelevant
Ballots for apparently "nothing tangible".


Chris Benham

 



Fri Dec 28 07:12:42 PST 2007 
Chris,

--- Chris Benham <cbenhamau at yahoo.com.au> a écrit :
> Kevin Venzke wrote:
> 
> "Try this method (an IRV variant) for example:

By the way, I have named this method "Instant VFA
Runoff."

> The voter ranks the candidates. Full ranking or
> truncation are allowed; equal ranking is not
allowed.
> 
> Say that X is the number of candidates still in the
> running.
> 
> While X>1:
> 
> If more than half of the original count of ballots
> rank candidate C in the Xth position (i.e. strictly
> last among candidates remaining), then eliminate C.
> Otherwise eliminate the candidate with the fewest
top
> preferences as in IRV.
> 
> End while.
> 
> Elect the remaining candidate."
> 
> Chris replies:
>
> Kevin,
> It seems to me that the specification of "more than
> half the original count of ballots" instead of "more
> than half the unexhausted ballots" causes this to
fail
> Independence from Irrelevant Ballots(IIB). What
> compensating advantage do you get by doing that?

Probably nothing tangible, however it seemed safer to
specify the method in this way, and it also seemed to
be more obviously in the spirit of finding the
"median" option.

> In the 49A,24B,27C>B scenario you have long held
that
> A shouldn't win because A has the only
> majority-strength pairwise loss (to B). And yet no
> candidate is ranked "strictly last" on more than
half
> the ballots so nothing stops B from being eliminated
> and A winning just like in regular IRV.

True. I find that very unfortunate about this method.

The two-round version of this method would eliminate B
and give B's supporters the option to vote for C in
the second round if they desired.
Also, the first round would use a VFA ballot. B voters
would probably find it attractive to vote against A if
they expect that some A voters would
support B over C in the second round.

> I suggest this:
> 
> "Voters rank the candidates,truncation allowed,
> above-bottom equal ranking not allowed.
> 
> Until one candidate remains, eliminate candidates
one
> at a time according to these rules:
> 
> (1)If one or more of the (remaining) candidates are
> not ranked (among remaining candidates)above bottom
or
> equal-bottom on more than half the ballots that make
> some ranking distinction among remaining candidates,
> eliminate the one of these that is top-ranked (among
> remaining candidates) on the fewest ballots.

I think that this rule doesn't do quite as good a job
emulating "ladder voting," though. With my rule,
assuming that voters are sincere and are laid out
(with the candidates) on a one-dimensional spectrum,
there should always be (and can only be) one candidate
who can be eliminated due to bottom rankings. (Unless
there are ties.)

> (2)Otherwise eliminate the candidate that is
> top-ranked (among remaining candidates) on the
fewest
> ballots.
> 
> Elect the remaining candidate."
> 
> What do you think of that? This meets Sincere
Defense
> and keeps IRV's IIB while being much more
Condorcetish
> than regular IRV.

It's probably fine. Either method's vulnerability to
burial strategy should
be checked out, though.

What I like about mine is that even if burial strategy
is used to disqualify a candidate, it's undisputable
that the majority wanted this
candidate to be disqualified given the selection of
candidates remaining.The strategy doesn't seem to take
inappropriate advantage of other people's
differently-minded votes.

Kevin Venzke




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