Re: [EM] [CES #15255] Re: PAR: nearly-equivalent rules
2016-11-12 17:45 GMT-05:00 Neal McBurnett nealmcb@gmail.com:
I haven't been paying that much attention. But this definition doesn't
define what this means "a rival is explicitly rejected". Is "rejected" the
opposite of "viable"? Or does it mean that no other voter cast any
"reject" vote for any other candidate? Or ???
If candidates are ABCD, a ballot that prefers A and leaves the rest blank
counts as rejecting BCD, but one that prefers A and rejects B and leaves
the rest blank counts as accepting CD.
So if I have an "accept" on a ballot that doesn't "prefer" the leader,
that means 0 points?
Since votes depend on how other votes are interpreted and who the leader
is, is the tally guaranteed to be attracted to a single stable equilibrium
tally?
Thanks,
-Neal
On Sat, Nov 12, 2016 at 05:27:53PM -0500, Jameson Quinn wrote:
I think this is the best phrasing I've come up with so far for PAR. I
think it's not exactly equivalent to the definitions I've
given before, but it is close enough to meet all the same properties and
give the same result in any basic scenario type.
Prefer Accept Reject (PAR) voting works as follows:
- Voters can Prefer, Accept, or Reject each candidate. Blanks count as
"Reject" if no rival is explicitly rejected; otherwise,
blank is "Accept".
- Candidates with at least 25% Prefer, and no more than 50% reject,
are "viable". The most-preferred viable candidate (if any) is
the leader.
- Each "prefer" is worth 1 point. For viable candidates, each "accept"
on a ballot which doesn't prefer the leader is also worth
1 point. Most points wins.
2016-11-12 13:47 GMT-05:00 Jameson Quinn jameson.quinn@gmail.com:
Thinking about PAR and the electoral college, I realized that there
is a different way to state the PAR rules:
1. Voters can Prefer, Accept, or Reject each candidate. Default is
"Reject" for voters who do not explicitly reject any
candidates, and "Accept" otherwise.
2. A candidate is "viable" if they are rejected by under 50%.
3. Each ballot gives 1 point to each candidate it prefers. Ballots
which prefer no viable candidates also give 1 point to each
candidate they accept, so long as that candidate is preferred by
at least 25%.
4. Now find the viable candidate with the most points, if any, and
redo step 3 from scratch as if only that candidate were
viable.
5. The winner is the candidate with the most points.
This could potentially differ from PAR in that it waits slightly
longer to "reveal" the preferences of candidates with under
25% preferences. In practice, I doubt this would typically make any
difference.
The procedure above is more complicated than PAR's, but the
advantage is that it produces counts which include the disqualified
candidates, and thus is suitable for combining with totals from
non-PAR systems such as approval, plurality, or
"pre-elimination totals" from IRV.
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Yet another revision of the rules. This one fixes it so that, if no
candidates pass both thresholds, "accept" votes count.
Prefer Accept Reject (PAR) voting works as follows:
-
Voters Prefer, Accept, or Reject each candidate. On ballots which
don't explicitly use "Reject", blanks count as "Reject"; otherwise, blanks
count as "Accept". -
Of the candidates that are both "viable" (at least 25% Prefer) and
"acceptable" (no more than 50% reject), the one with most "Prefer"s is
called the leader. - Each "Prefer" is worth 1 point. For viable candidates, each "Accept"
on a ballot which doesn't prefer the leader is also worth 1 point. Most
points wins.
If I could do it without it sounding too complicated, I'd make it so that
explicit "accept" votes can count for non-viable candidates. But I don't
think it's worth even the minor extra complication it would take to explain
that.
Note that changing the above system so that it passes FBC requires only
giving a "prefer for the purposes of step 3, but count step 2 as if I
rejected" option.
I think this system is pretty great in outcomes; and that, while it's
certainly not the simplest method, it's not too complex.
2016-11-12 23:33 GMT-05:00 Jameson Quinn jameson.quinn@gmail.com:
2016-11-12 17:45 GMT-05:00 Neal McBurnett nealmcb@gmail.com:
I haven't been paying that much attention. But this definition doesn't
define what this means "a rival is explicitly rejected". Is "rejected" the
opposite of "viable"? Or does it mean that no other voter cast any
"reject" vote for any other candidate? Or ???
If candidates are ABCD, a ballot that prefers A and leaves the rest blank
counts as rejecting BCD, but one that prefers A and rejects B and leaves
the rest blank counts as accepting CD.
So if I have an "accept" on a ballot that doesn't "prefer" the leader,
that means 0 points?
Since votes depend on how other votes are interpreted and who the leader
is, is the tally guaranteed to be attracted to a single stable equilibrium
tally?
Thanks,
-Neal
On Sat, Nov 12, 2016 at 05:27:53PM -0500, Jameson Quinn wrote:
I think this is the best phrasing I've come up with so far for PAR. I
think it's not exactly equivalent to the definitions I've
given before, but it is close enough to meet all the same properties
and give the same result in any basic scenario type.
Prefer Accept Reject (PAR) voting works as follows:
- Voters can Prefer, Accept, or Reject each candidate. Blanks count
as "Reject" if no rival is explicitly rejected; otherwise,
blank is "Accept".
- Candidates with at least 25% Prefer, and no more than 50% reject,
are "viable". The most-preferred viable candidate (if any) is
the leader.
- Each "prefer" is worth 1 point. For viable candidates, each
"accept" on a ballot which doesn't prefer the leader is also worth
1 point. Most points wins.
2016-11-12 13:47 GMT-05:00 Jameson Quinn jameson.quinn@gmail.com:
Thinking about PAR and the electoral college, I realized that there
is a different way to state the PAR rules:
1. Voters can Prefer, Accept, or Reject each candidate. Default is
"Reject" for voters who do not explicitly reject any
candidates, and "Accept" otherwise.
2. A candidate is "viable" if they are rejected by under 50%.
3. Each ballot gives 1 point to each candidate it prefers. Ballots
which prefer no viable candidates also give 1 point to each
candidate they accept, so long as that candidate is preferred
by at least 25%.
4. Now find the viable candidate with the most points, if any, and
redo step 3 from scratch as if only that candidate were
viable.
5. The winner is the candidate with the most points.
This could potentially differ from PAR in that it waits slightly
longer to "reveal" the preferences of candidates with under
25% preferences. In practice, I doubt this would typically make any
difference.
The procedure above is more complicated than PAR's, but the
advantage is that it produces counts which include the disqualified
candidates, and thus is suitable for combining with totals from
non-PAR systems such as approval, plurality, or
"pre-elimination totals" from IRV.
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I'm still working on getting PAR expressed in the best format. Here's the
latest:
-
Voters Prefer, Accept, or Reject each candidate. On ballots which
don't explicitly use "Reject", or for candidates with less than 25%
"Prefer", blanks count as "Reject"; otherwise, blanks count as "Accept". - Tally 1 point for each "Prefer" for each candidate.
- Out of the candidates (if any) with no more than 50% "Reject", find
the one with the most points. For every ballot which doesn't "Prefer"
this frontrunner, add 1 point for each "Accept". - If the frontrunner changed, add 1 for each "Accept" that's not yet
tallied (the ones which "Prefer" the original frontrunner). Most points
wins.
I now believe that the system as expressed above meets the voted majority
Condorcet criterion. Which means that FBPPAR (almost) meets both FBC and
voted majority Condorcet! Impossible, you say? No; approval meets both of
these criteria (because it reduces "voted Condorcet" to a triviality), and
FBPPAR reduces to approval when voters strategize expecting a Condorcet
cycle.
What do I mean by "(almost)" above? Well, FBPPAR allows voters to rate a
candidate as "prefer, but do not make them frontrunner because of my vote".
This is useful for cyclical and near-cyclical situations (that is, for A>B
voters who know that most B votes are B>C and that C beats A). But if this
option is used in cases where it is not actually strategic, it breaks the
voted majority Condorcet property.
So FBPPAR is a system that meets FBC; deals with center squeeze via a
fairly strong Condorcet-like property; deals with chicken dilemma without a
slippery slope; can be counted in at most 3 rounds, each of which is O(N)
summable; meets majority and mutual majority; meets a weakened version of
later-no-help; outputs tallies that are summable with other approval
tallies; and is basically all-around awesome. Personally, I feel that
FBPPAR essentially dominates other 3-rank systems in terms of strategic
properties; and that PAR is, in the real world, a very close approximation
of FBPPAR that's justified by its greater simplicity.
2016-11-13 18:04 GMT-05:00 Jameson Quinn jameson.quinn@gmail.com:
Yet another revision of the rules. This one fixes it so that, if no
candidates pass both thresholds, "accept" votes count.
Prefer Accept Reject (PAR) voting works as follows:
1. *Voters Prefer, Accept, or Reject each candidate.* On ballots which
don't explicitly use "Reject", blanks count as "Reject"; otherwise, blanks
count as "Accept".
2. *Of the candidates that are both "viable"* (at least 25% Prefer) *and
"acceptable"* (no more than 50% reject), *the one with most "Prefer"s
is called the leader.*
3. Each "Prefer" is worth 1 point. For viable candidates, each
"Accept" on a ballot which doesn't prefer the leader is also worth 1 point. *Most
points wins.*
If I could do it without it sounding too complicated, I'd make it so that
explicit "accept" votes can count for non-viable candidates. But I don't
think it's worth even the minor extra complication it would take to explain
that.
Note that changing the above system so that it passes FBC requires only
giving a "prefer for the purposes of step 3, but count step 2 as if I
rejected" option.
I think this system is pretty great in outcomes; and that, while it's
certainly not the simplest method, it's not too complex.
2016-11-12 23:33 GMT-05:00 Jameson Quinn jameson.quinn@gmail.com:
2016-11-12 17:45 GMT-05:00 Neal McBurnett nealmcb@gmail.com:
I haven't been paying that much attention. But this definition doesn't
define what this means "a rival is explicitly rejected". Is "rejected" the
opposite of "viable"? Or does it mean that no other voter cast any
"reject" vote for any other candidate? Or ???
If candidates are ABCD, a ballot that prefers A and leaves the rest blank
counts as rejecting BCD, but one that prefers A and rejects B and leaves
the rest blank counts as accepting CD.
So if I have an "accept" on a ballot that doesn't "prefer" the leader,
that means 0 points?
Since votes depend on how other votes are interpreted and who the leader
is, is the tally guaranteed to be attracted to a single stable equilibrium
tally?
Thanks,
-Neal
On Sat, Nov 12, 2016 at 05:27:53PM -0500, Jameson Quinn wrote:
I think this is the best phrasing I've come up with so far for PAR. I
think it's not exactly equivalent to the definitions I've
given before, but it is close enough to meet all the same properties
and give the same result in any basic scenario type.
Prefer Accept Reject (PAR) voting works as follows:
- Voters can Prefer, Accept, or Reject each candidate. Blanks count
as "Reject" if no rival is explicitly rejected; otherwise,
blank is "Accept".
- Candidates with at least 25% Prefer, and no more than 50% reject,
are "viable". The most-preferred viable candidate (if any) is
the leader.
- Each "prefer" is worth 1 point. For viable candidates, each
"accept" on a ballot which doesn't prefer the leader is also worth
1 point. Most points wins.
2016-11-12 13:47 GMT-05:00 Jameson Quinn jameson.quinn@gmail.com:
Thinking about PAR and the electoral college, I realized that
there is a different way to state the PAR rules:
1. Voters can Prefer, Accept, or Reject each candidate. Default
is "Reject" for voters who do not explicitly reject any
candidates, and "Accept" otherwise.
2. A candidate is "viable" if they are rejected by under 50%.
3. Each ballot gives 1 point to each candidate it prefers.
Ballots which prefer no viable candidates also give 1 point to each
candidate they accept, so long as that candidate is preferred
by at least 25%.
4. Now find the viable candidate with the most points, if any,
and redo step 3 from scratch as if only that candidate were
viable.
5. The winner is the candidate with the most points.
This could potentially differ from PAR in that it waits slightly
longer to "reveal" the preferences of candidates with under
25% preferences. In practice, I doubt this would typically make
any difference.
The procedure above is more complicated than PAR's, but the
advantage is that it produces counts which include the disqualified
candidates, and thus is suitable for combining with totals from
non-PAR systems such as approval, plurality, or
"pre-elimination totals" from IRV.
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The first round of Step 3 could be made summable with the addition of an
NxN array where row i accumulates, from a ballot that does not Prefer the
i-th candidate, Accept points cast for any candidates besides the i-th
candidate.
I'm not sure if that same array could be used for step 4, however. In
fact, step 4 is not entirely clear to me.
Ted
On Mon, Nov 14, 2016 at 10:14 AM, Jameson Quinn jameson.quinn@gmail.com
wrote:
I'm still working on getting PAR expressed in the best format. Here's the
latest:
1. *Voters Prefer, Accept, or Reject each candidate.* On ballots which
don't explicitly use "Reject", or for candidates with less than 25%
"Prefer", blanks count as "Reject"; otherwise, blanks count as "Accept".
2. *Tally 1 point for each "Prefer"* for each candidate.
3. Out of the candidates (if any) with no more than 50% "Reject", find
the one with the most points. *For every ballot which doesn't "Prefer"
this frontrunner, add 1 point for each "Accept".*
4. If the frontrunner changed, add 1 for each "Accept" that's not yet
tallied (the ones which "Prefer" the original frontrunner). *Most
points wins.*
I now believe that the system as expressed above meets the voted majority
Condorcet criterion. Which means that FBPPAR (almost) meets both FBC and
voted majority Condorcet! Impossible, you say? No; approval meets both of
these criteria (because it reduces "voted Condorcet" to a triviality), and
FBPPAR reduces to approval when voters strategize expecting a Condorcet
cycle.
What do I mean by "(almost)" above? Well, FBPPAR allows voters to rate a
candidate as "prefer, but do not make them frontrunner because of my vote".
This is useful for cyclical and near-cyclical situations (that is, for A>B
voters who know that most B votes are B>C and that C beats A). But if this
option is used in cases where it is not actually strategic, it breaks the
voted majority Condorcet property.
So FBPPAR is a system that meets FBC; deals with center squeeze via a
fairly strong Condorcet-like property; deals with chicken dilemma without a
slippery slope; can be counted in at most 3 rounds, each of which is O(N)
summable; meets majority and mutual majority; meets a weakened version of
later-no-help; outputs tallies that are summable with other approval
tallies; and is basically all-around awesome. Personally, I feel that
FBPPAR essentially dominates other 3-rank systems in terms of strategic
properties; and that PAR is, in the real world, a very close approximation
of FBPPAR that's justified by its greater simplicity.
2016-11-13 18:04 GMT-05:00 Jameson Quinn jameson.quinn@gmail.com:
Yet another revision of the rules. This one fixes it so that, if no
candidates pass both thresholds, "accept" votes count.
Prefer Accept Reject (PAR) voting works as follows:
1. *Voters Prefer, Accept, or Reject each candidate.* On ballots
which don't explicitly use "Reject", blanks count as "Reject"; otherwise,
blanks count as "Accept".
2. *Of the candidates that are both "viable"* (at least 25% Prefer) *and
"acceptable"* (no more than 50% reject), *the one with most "Prefer"s
is called the leader.*
3. Each "Prefer" is worth 1 point. For viable candidates, each
"Accept" on a ballot which doesn't prefer the leader is also worth 1 point. *Most
points wins.*
If I could do it without it sounding too complicated, I'd make it so that
explicit "accept" votes can count for non-viable candidates. But I don't
think it's worth even the minor extra complication it would take to explain
that.
Note that changing the above system so that it passes FBC requires only
giving a "prefer for the purposes of step 3, but count step 2 as if I
rejected" option.
I think this system is pretty great in outcomes; and that, while it's
certainly not the simplest method, it's not too complex.
2016-11-12 23:33 GMT-05:00 Jameson Quinn jameson.quinn@gmail.com:
2016-11-12 17:45 GMT-05:00 Neal McBurnett nealmcb@gmail.com:
I haven't been paying that much attention. But this definition doesn't
define what this means "a rival is explicitly rejected". Is "rejected" the
opposite of "viable"? Or does it mean that no other voter cast any
"reject" vote for any other candidate? Or ???
If candidates are ABCD, a ballot that prefers A and leaves the rest
blank counts as rejecting BCD, but one that prefers A and rejects B and
leaves the rest blank counts as accepting CD.
So if I have an "accept" on a ballot that doesn't "prefer" the leader,
that means 0 points?
Since votes depend on how other votes are interpreted and who the
leader is, is the tally guaranteed to be attracted to a single stable
equilibrium tally?
Thanks,
-Neal
On Sat, Nov 12, 2016 at 05:27:53PM -0500, Jameson Quinn wrote:
I think this is the best phrasing I've come up with so far for PAR. I
think it's not exactly equivalent to the definitions I've
given before, but it is close enough to meet all the same properties
and give the same result in any basic scenario type.
Prefer Accept Reject (PAR) voting works as follows:
- Voters can Prefer, Accept, or Reject each candidate. Blanks count
as "Reject" if no rival is explicitly rejected; otherwise,
blank is "Accept".
- Candidates with at least 25% Prefer, and no more than 50% reject,
are "viable". The most-preferred viable candidate (if any) is
the leader.
- Each "prefer" is worth 1 point. For viable candidates, each
"accept" on a ballot which doesn't prefer the leader is also worth
1 point. Most points wins.
2016-11-12 13:47 GMT-05:00 Jameson Quinn jameson.quinn@gmail.com:
Thinking about PAR and the electoral college, I realized that
there is a different way to state the PAR rules:
1. Voters can Prefer, Accept, or Reject each candidate. Default
is "Reject" for voters who do not explicitly reject any
candidates, and "Accept" otherwise.
2. A candidate is "viable" if they are rejected by under 50%.
3. Each ballot gives 1 point to each candidate it prefers.
Ballots which prefer no viable candidates also give 1 point to each
candidate they accept, so long as that candidate is preferred
by at least 25%.
4. Now find the viable candidate with the most points, if any,
and redo step 3 from scratch as if only that candidate were
viable.
5. The winner is the candidate with the most points.
This could potentially differ from PAR in that it waits slightly
longer to "reveal" the preferences of candidates with under
25% preferences. In practice, I doubt this would typically make
any difference.
The procedure above is more complicated than PAR's, but the
advantage is that it produces counts which include the disqualified
candidates, and thus is suitable for combining with totals from
non-PAR systems such as approval, plurality, or
"pre-elimination totals" from IRV.
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Ted is right. This latest version of PAR is in fact O(N²) summable as a
whole. The tallies you need:
P(x): the number of "prefers" for X
a(x): the number of explicit "accepts" for X
B(x): the number of blanks for X on ballots that have at least one explicit
"reject"
A(x,y):the number of "accepts" for X on ballots that do not prefer Y
Here are the steps expressed using those quantities:
- Define A(x) to be a(x) for x such that P(x)<25%, and a(x)+B(x) for all
other x. Define R(x) to be N-P(x)-A(x). - If there are any candidates such that R(x)<=50%, find the y that
maximizes P(y)*I(R(y)<=50%) (where I(...) is 1 if ... is true and 0
otherwise). - Define T(x) as P(x)+A(x,y).
- If y maximizes T(y), then y wins. Otherwise, the winner is the candidate
z who maximizes N-R(z) (or equivalently, P(z)+A(z).)
2016-11-14 14:13 GMT-05:00 Ted Stern dodecatheon@gmail.com:
The first round of Step 3 could be made summable with the addition of an
NxN array where row i accumulates, from a ballot that does not Prefer the
i-th candidate, Accept points cast for any candidates besides the i-th
candidate.
I'm not sure if that same array could be used for step 4, however. In
fact, step 4 is not entirely clear to me.
Ted
On Mon, Nov 14, 2016 at 10:14 AM, Jameson Quinn jameson.quinn@gmail.com
wrote:
I'm still working on getting PAR expressed in the best format. Here's the
latest:
1. *Voters Prefer, Accept, or Reject each candidate.* On ballots
which don't explicitly use "Reject", or for candidates with less than 25%
"Prefer", blanks count as "Reject"; otherwise, blanks count as "Accept".
2. *Tally 1 point for each "Prefer"* for each candidate.
3. Out of the candidates (if any) with no more than 50% "Reject",
find the one with the most points. *For every ballot which doesn't
"Prefer" this frontrunner, add 1 point for each "Accept".*
4. If the frontrunner changed, add 1 for each "Accept" that's not yet
tallied (the ones which "Prefer" the original frontrunner). *Most
points wins.*
I now believe that the system as expressed above meets the voted majority
Condorcet criterion. Which means that FBPPAR (almost) meets both FBC and
voted majority Condorcet! Impossible, you say? No; approval meets both of
these criteria (because it reduces "voted Condorcet" to a triviality), and
FBPPAR reduces to approval when voters strategize expecting a Condorcet
cycle.
What do I mean by "(almost)" above? Well, FBPPAR allows voters to rate a
candidate as "prefer, but do not make them frontrunner because of my vote".
This is useful for cyclical and near-cyclical situations (that is, for A>B
voters who know that most B votes are B>C and that C beats A). But if this
option is used in cases where it is not actually strategic, it breaks the
voted majority Condorcet property.
So FBPPAR is a system that meets FBC; deals with center squeeze via a
fairly strong Condorcet-like property; deals with chicken dilemma without a
slippery slope; can be counted in at most 3 rounds, each of which is O(N)
summable; meets majority and mutual majority; meets a weakened version of
later-no-help; outputs tallies that are summable with other approval
tallies; and is basically all-around awesome. Personally, I feel that
FBPPAR essentially dominates other 3-rank systems in terms of strategic
properties; and that PAR is, in the real world, a very close approximation
of FBPPAR that's justified by its greater simplicity.
2016-11-13 18:04 GMT-05:00 Jameson Quinn jameson.quinn@gmail.com:
Yet another revision of the rules. This one fixes it so that, if no
candidates pass both thresholds, "accept" votes count.
Prefer Accept Reject (PAR) voting works as follows:
1. *Voters Prefer, Accept, or Reject each candidate.* On ballots
which don't explicitly use "Reject", blanks count as "Reject"; otherwise,
blanks count as "Accept".
2. *Of the candidates that are both "viable"* (at least 25% Prefer) *and
"acceptable"* (no more than 50% reject), *the one with most
"Prefer"s is called the leader.*
3. Each "Prefer" is worth 1 point. For viable candidates, each
"Accept" on a ballot which doesn't prefer the leader is also worth 1 point. *Most
points wins.*
If I could do it without it sounding too complicated, I'd make it so
that explicit "accept" votes can count for non-viable candidates. But I
don't think it's worth even the minor extra complication it would take to
explain that.
Note that changing the above system so that it passes FBC requires only
giving a "prefer for the purposes of step 3, but count step 2 as if I
rejected" option.
I think this system is pretty great in outcomes; and that, while it's
certainly not the simplest method, it's not too complex.
2016-11-12 23:33 GMT-05:00 Jameson Quinn jameson.quinn@gmail.com:
2016-11-12 17:45 GMT-05:00 Neal McBurnett nealmcb@gmail.com:
I haven't been paying that much attention. But this definition
doesn't define what this means "a rival is explicitly rejected". Is
"rejected" the opposite of "viable"? Or does it mean that no other voter
cast any "reject" vote for any other candidate? Or ???
If candidates are ABCD, a ballot that prefers A and leaves the rest
blank counts as rejecting BCD, but one that prefers A and rejects B and
leaves the rest blank counts as accepting CD.
So if I have an "accept" on a ballot that doesn't "prefer" the leader,
that means 0 points?
Since votes depend on how other votes are interpreted and who the
leader is, is the tally guaranteed to be attracted to a single stable
equilibrium tally?
Thanks,
-Neal
On Sat, Nov 12, 2016 at 05:27:53PM -0500, Jameson Quinn wrote:
I think this is the best phrasing I've come up with so far for PAR.
I think it's not exactly equivalent to the definitions I've
given before, but it is close enough to meet all the same properties
and give the same result in any basic scenario type.
Prefer Accept Reject (PAR) voting works as follows:
- Voters can Prefer, Accept, or Reject each candidate. Blanks
count as "Reject" if no rival is explicitly rejected; otherwise,
blank is "Accept".
- Candidates with at least 25% Prefer, and no more than 50%
reject, are "viable". The most-preferred viable candidate (if any) is
the leader.
- Each "prefer" is worth 1 point. For viable candidates, each
"accept" on a ballot which doesn't prefer the leader is also worth
1 point. Most points wins.
2016-11-12 13:47 GMT-05:00 Jameson Quinn jameson.quinn@gmail.com:
Thinking about PAR and the electoral college, I realized that
there is a different way to state the PAR rules:
1. Voters can Prefer, Accept, or Reject each candidate. Default
is "Reject" for voters who do not explicitly reject any
candidates, and "Accept" otherwise.
2. A candidate is "viable" if they are rejected by under 50%.
3. Each ballot gives 1 point to each candidate it prefers.
Ballots which prefer no viable candidates also give 1 point to each
candidate they accept, so long as that candidate is
preferred by at least 25%.
4. Now find the viable candidate with the most points, if any,
and redo step 3 from scratch as if only that candidate were
viable.
5. The winner is the candidate with the most points.
This could potentially differ from PAR in that it waits slightly
longer to "reveal" the preferences of candidates with under
25% preferences. In practice, I doubt this would typically make
any difference.
The procedure above is more complicated than PAR's, but the
advantage is that it produces counts which include the disqualified
candidates, and thus is suitable for combining with totals from
non-PAR systems such as approval, plurality, or
"pre-elimination totals" from IRV.
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