Heitzig consensus and brinkmanship
The other day, I was thinking about the Heitzig consensus mechanism --
the one where you submit a favorite ballot and a consensus ballot, and
if there's unanimity in favor of the consensus, then it wins, otherwise
you run Random Ballot on the favorites.
I had a thought: is this method susceptible to a sort of brinkmanship
strategy? Suppose a faction wants to pull the consensus in its
direction. It declares that unless it gets a concession on the
consensus, it will dishonestly set its favorite option to something
extremely damaging, so as to make the random ballot option all the worse
for everybody involved. Like in a standoff, the faction doesn't actually
want the worse option to be chosen, it just wants the threat to be credible.
There's a typical defection dynamic to this, too. Any given faction can
amplify its influence by threatening disaster if it doesn't get what it
wants. However, if every faction does so, then the result is certain
destruction.
But then again, perhaps the problem only exists if the favorite votes
are public. Suppose they are anonymous. Then a faction may declare that
it is willing to risk disaster to pull the consensus in its direction.
However, since the faction doesn't want disaster to strike, it's better
to declare such a threat but not follow up on it, because when the vote
happens, the faction can only lose by voting something disastrous as its
favorite. But the other factions know this, so they won't consider the
threat to have any force, and so the problem disappears.
Is it that easy?
-km
Hi Kristofer, I have a feeling that in a setting so contentious that a faction would considermaking such threats, the odds of achieving a consensus result are already really small.I think factions would always doubt that the other factions are giving up enough. I picturean informal pre-vote debate about where the consensus should be. The mechanismmight push selection towards the median voter (unless in practice the mechanism hasso little chance of operating that people forget about it), but people wouldn't agree wherethe median is. So I think people would assume consensus is impossible.
If the number of voters is small and known, maybe it would be different. But I'm reallynot sure... Suppose via PR the voters elect five representative voters to play this game.Five seems like enough where a spectrum of views might be represented, where thevoter on one extreme really doesn't want to see his counterpart win. But it's easy to imagine that the median option of the five offers the same utility to the extremes as rolling the dice. I could also imagine political value to refusing to endorse the consensusand hanging on to a chance to win.
Maybe I've overlooked something though.
Going off topic, the idea I like here is to require each voter to nominate a majority ofthe voters (as though they would form a government). The most-nominated voterdetermines the outcome of the question. In this way, defection requires a potentiallydangerous form of burial.
Kevin
Le dimanche 5 juillet 2020 à 18:28:44 UTC−5, Kristofer Munsterhjelm <km_elmet@t-online.de> a écrit :
The other day, I was thinking about the Heitzig consensus mechanism --
the one where you submit a favorite ballot and a consensus ballot, and
if there's unanimity in favor of the consensus, then it wins, otherwise
you run Random Ballot on the favorites.
I had a thought: is this method susceptible to a sort of brinkmanship
strategy? Suppose a faction wants to pull the consensus in its
direction. It declares that unless it gets a concession on the
consensus, it will dishonestly set its favorite option to something
extremely damaging, so as to make the random ballot option all the worse
for everybody involved. Like in a standoff, the faction doesn't actually
want the worse option to be chosen, it just wants the threat to be credible.
There's a typical defection dynamic to this, too. Any given faction can
amplify its influence by threatening disaster if it doesn't get what it
wants. However, if every faction does so, then the result is certain
destruction.
But then again, perhaps the problem only exists if the favorite votes
are public. Suppose they are anonymous. Then a faction may declare that
it is willing to risk disaster to pull the consensus in its direction.
However, since the faction doesn't want disaster to strike, it's better
to declare such a threat but not follow up on it, because when the vote
happens, the faction can only lose by voting something disastrous as its
favorite. But the other factions know this, so they won't consider the
threat to have any force, and so the problem disappears.
Is it that easy?
-km
Election-Methods mailing list - see https://electorama.com/em for list info
On 07/07/2020 03.20, Kevin Venzke wrote:
Hi Kristofer, I have a feeling that in a setting so contentious that
a faction would consider making such threats, the odds of achieving a
consensus result are already really small. I think factions would
always doubt that the other factions are giving up enough. I picture
an informal pre-vote debate about where the consensus should be. The
mechanism might push selection towards the median voter (unless in
practice the mechanism has so little chance of operating that people
forget about it), but people wouldn't agree where the median is. So I
think people would assume consensus is impossible.
You are probably right. If there is an easy consensus to be had, (and
the participants are honest,) then nobody would feel the need to make
threats like that.
I was thinking about the possibility of using the mechanism to direct a
government or organization to act in a minmax manner: one that intend to
make the worst off best off, rather than improve the condition of the
median voter. From what I remember, Jobst and Forest were originally
trying to find a method to avoid a majority dictatorship, so my idea is
in a way to consistently take that to its logical conclusion. If the
state or the organization must pay attention to every voter, or to a
supermajority of them, then it can't afford to leave some of them badly off.
But if it's to be used as a part of normal operating procedure, then it
has to resist strategy to some degree, and it can't take the whole
organization or state down with it at the first sign of trouble. So if
the brinkmanship scenario is a problem, then either the mechanism has to
be augmented to stop it being a problem, or the assembly has to somehow
be able to keep the peace enough that politics will never become that
contentious to begin with.
If the number of voters is small and known, maybe it would be
different. But I'm really not sure... Suppose via PR the voters elect
five representative voters to play this game. Five seems like enough
where a spectrum of views might be represented, where the voter on
one extreme really doesn't want to see his counterpart win. But it's
easy to imagine that the median option of the five offers the same
utility to the extremes as rolling the dice. I could also imagine
political value to refusing to endorse the consensus and hanging on
to a chance to win.
Yes, that is a possibility - that a way out is to make the consensus
option at least as good on expectation as the roll of the dice,
discounted by whatever risk aversion exists.
That's an important point, I think. The consensus option doesn't have to
be extremely good. For it to be chosen, it just has to be preferred to
rolling the dice by everyone. If it's barely better, that's still good
enough to make it pass.
Maybe I've overlooked something though.
Going off topic, the idea I like here is to require each voter to
nominate a majority of the voters (as though they would form a
government). The most-nominated voter determines the outcome of the
question. In this way, defection requires a potentially dangerous
form of burial.
Wouldn't that give a coordinated majority the ability to control the
outcome? Or am I missing something?
Hi Kristofer,
Le mardi 14 juillet 2020 à 18:40:19 UTC−5, Kristofer Munsterhjelm km_elmet@t-online.de a écrit :
I was thinking about the possibility of using the mechanism to direct a
government or organization to act in a minmax manner: one that intend to
make the worst off best off, rather than improve the condition of the
median voter.
Just to interject quickly. To my mind these two things are (naively) the same, andif results matched the preference of the median voter you would have a goodthing. What I expect instead, with two factions fighting over who can capture a majority, is that the factions don't propose (or don't enact) the median position.They want the vote of that position, and those voters can come to the victory party,but they won't be in control.
From what I remember, Jobst and Forest were originally
trying to find a method to avoid a majority dictatorship, so my idea is
in a way to consistently take that to its logical conclusion. If the
state or the organization must pay attention to every voter, or to a
supermajority of them, then it can't afford to leave some of them badly off.
But if it's to be used as a part of normal operating procedure, then it
has to resist strategy to some degree, and it can't take the whole
organization or state down with it at the first sign of trouble. So if
the brinkmanship scenario is a problem, then either the mechanism has to
be augmented to stop it being a problem, or the assembly has to somehow
be able to keep the peace enough that politics will never become that
contentious to begin with.
It seems like a tall order...
Yes, that is a possibility - that a way out is to make the consensus
option at least as good on expectation as the roll of the dice,
discounted by whatever risk aversion exists.
That's an important point, I think. The consensus option doesn't have to
be extremely good. For it to be chosen, it just has to be preferred to
rolling the dice by everyone. If it's barely better, that's still good
enough to make it pass.
I think that may be true (if we rule out, as I say, a value to being perceivedas unwilling to compromise), but I wonder how often such a consensusoption could be expected to exist? I picture the math of it very simply butit seems like it should be nearly a wash.
When you say "to make the consensus option at least as good" do youenvision some kind of mechanism that could actually improve what theconsensus option is? Or maybe, easier to imagine: a rule that imposes some kind of universal penalty if consensus isn't achieved. A forfeiture of office seems like the most obvious.
Maybe I've overlooked something though.
Going off topic, the idea I like here is to require each voter to
nominate a majority of the voters (as though they would form a
government). The most-nominated voter determines the outcome of the
question. In this way, defection requires a potentially dangerous
form of burial.
Wouldn't that give a coordinated majority the ability to control the
outcome? Or am I missing something?
They certainly can ensure that one of them wins it, but not which one ofthem wins it. Imagine a 55:45 complete partisan split. The 55 can purelyvote for themselves (i.e. each casts 51-55 approvals). But the 45 willeach have to vote for 6+ of the 55. If there really is no difference among the 55, then nothing has been gained. You have to hope there is a"moderate wing" within the 55 that the 6+ votes can be given to.
Kevin
On 16/07/2020 02.02, Kevin Venzke wrote:
Hi Kristofer,
Le mardi 14 juillet 2020 à 18:40:19 UTC−5, Kristofer Munsterhjelm
km_elmet@t-online.de a écrit :
I was thinking about the possibility of using the mechanism to direct a
government or organization to act in a minmax manner: one that intend to
make the worst off best off, rather than improve the condition of the
median voter.
Just to interject quickly. To my mind these two things are (naively)
the same, and if results matched the preference of the median voter
you would have a good thing. What I expect instead, with two factions
fighting over who can capture a majority, is that the factions don't
propose (or don't enact) the median position. They want the vote of
that position, and those voters can come to the victory party, but
they won't be in control.
Doesn't the pizza election show that these are not the same? Suppose the
utilities are:
7 voters: Pepperoni 9, Mushroom 8
3 voters: Pepperoni 0, Mushroom 9
The median voter prefers pepperoni. But a minmax outcome is the one that
leaves the worst-off voter best off, and that's mushroom. In this case,
the Heitzig consensus fails to deliver minmax, because the 70%
supermajority prefers a random ballot to mushroom. But if it's
two-sided, say:
6 voters: Pepperoni 9, Mushroom 8, Anchovies 0
2 voters: Anchovies 9, Mushroom 8, Pepperoni 0
2 voters: Anchovies 0, Mushroom 9, Pepperoni 0
then the outcome of a random ballot is 0.6 * Pepperoni + 0.2 * Anchovies
- 0.2 * Mushroom. The expected score is thus:
To the group of 6 pepperoni voters: 7.0
To the group of 2 anchovy voters: 3.4
To the group of 2 mushroom voters: 1.8
and everybody prefers mushroom to this, so it's in everybody's interest
to choose mushroom as the consensus. Hence the minmax option wins, but
in a majoritarian election method or a strategic Range election,
Pepperoni wins.
From what I remember, Jobst and Forest were originally
trying to find a method to avoid a majority dictatorship, so my idea is
in a way to consistently take that to its logical conclusion. If the
state or the organization must pay attention to every voter, or to a
supermajority of them, then it can't afford to leave some of them
badly off.
But if it's to be used as a part of normal operating procedure, then it
has to resist strategy to some degree, and it can't take the whole
organization or state down with it at the first sign of trouble. So if
the brinkmanship scenario is a problem, then either the mechanism has to
be augmented to stop it being a problem, or the assembly has to somehow
be able to keep the peace enough that politics will never become that
contentious to begin with.
It seems like a tall order...
Yes. I don't know of any other mechanisms that come as close as it does
to implementing minmax, so it would be really nice if it could be made
to work.
Yes, that is a possibility - that a way out is to make the consensus
option at least as good on expectation as the roll of the dice,
discounted by whatever risk aversion exists.
That's an important point, I think. The consensus option doesn't have to
be extremely good. For it to be chosen, it just has to be preferred to
rolling the dice by everyone. If it's barely better, that's still good
enough to make it pass.
I think that may be true (if we rule out, as I say, a value to being
perceived as unwilling to compromise), but I wonder how often such a
consensus option could be expected to exist? I picture the math of it
very simply but it seems like it should be nearly a wash.
When you say "to make the consensus option at least as good" do you
envision some kind of mechanism that could actually improve what the
consensus option is? Or maybe, easier to imagine: a rule that imposes
some kind of universal penalty if consensus isn't achieved. A forfeiture of
office seems like the most obvious.
I was thinking that the random ballot outcome can be quite bad. E.g. the
expected scores in the two-sided pizza election:
6 pepperoni voters: 7.0
2 anchovy voters: 3.4
2 mushroom voters: 1.8
If someone blinks (e.g. an anchovy voter mistakenly doesn't set mushroom
as the consensus option), then the outcome is not particularly good for
society as a whole. All we really need is the expectation of the
lottery to be less than the consensus option, while resisting strategy.
So in some ideal world, the expected value for the fair lottery would be
something along the lines of
6 pepperoni voters: 8 - epsilon
2 anchovy voters: 8 - epsilon
2 mushroom voters: 9 - epsilon
and even for very small epsilon, it would still be preferable to choose
the mushroom consensus option. But how to implement such a lottery, much
less in a strategy-resistant manner, I have no idea.
In a way, it's like the concept of MAD: if you give every voter his
personal doomsday button to push if he doesn't get a satisfactory
outcome, then minmax will happen if it's at all achievable. However, the
outcome should consensus be impossible is truly horrible. The better the
system can be in the "no consensus" case while leaving consensus
preferable, the better the method is.
The other side of that coin is what I said in the earlier post: if the
consensus option is always at least as good as a random ballot, then
it'll always be chosen. So making the structure around the mechanism
conducive to finding a consensus would also help.
We'd have to be careful that the alternative to consensus isn't biased,
though. "Forfeiting one's office" might well be, just like "status quo
prevails" is.
Hi Kristofer,
Le mercredi 29 juillet 2020 à 12:45:02 UTC−5, Kristofer Munsterhjelm km_elmet@t-online.de a écrit :
On 16/07/2020 02.02, Kevin Venzke wrote:
I was thinking about the possibility of using the mechanism to direct a
government or organization to act in a minmax manner: one that intend to
make the worst off best off, rather than improve the condition of the
median voter.
Just to interject quickly. To my mind these two things are (naively)
the same, and if results matched the preference of the median voter
you would have a good thing. What I expect instead, with two factions
fighting over who can capture a majority, is that the factions don't
propose (or don't enact) the median position. They want the vote of
that position, and those voters can come to the victory party, but
they won't be in control.
Doesn't the pizza election show that these are not the same? Suppose the
utilities are:
7 voters: Pepperoni 9, Mushroom 8
3 voters: Pepperoni 0, Mushroom 9
Absolutely it shows that they aren't exactly the same. I understand what you are saying,so it becomes maybe a terminology issue that may not be of interest. But for me there arethree concepts here:1. the minmax objective, as you say.
2. enacting the median voter's position, which is how I would interpret "improve the conditionof the median voter," though I understand this is not really the concept you are using inthe pizza example.3. the result you might expect from a majoritarian or strategic Range election, meaningmerely that the median voter will be included in the victorious majority.
You can see the potential for difference between 2 and 3 by putting "heavy pepperoni" and "light pepperoni" in your example and arranging it on a spectrum, placing a smallnumber of "light pepperoni" supporters at the median. It becomes unclear whether "light"will win under a majoritarian method. It's only clear that some pepperoni option will win.
What I mean by 1 and 2 being "naively the same" is that if you generate scenarios randomly in issue space, they are probably the same. Or at least similar enough thatif it's easier to address the problem by focusing on 2 and not 1, maybe that's worth it.
The pizza scenario highlights the situation where 1 differs from 2 and 3. But I think it'smore common that 3 is the outlier. That disturbs me because it seems that 2 should beachievable without even deviating from majoritarian principles.
When you say "to make the consensus option at least as good" do you
envision some kind of mechanism that could actually improve what the
consensus option is? Or maybe, easier to imagine: a rule that imposes
some kind of universal penalty if consensus isn't achieved. A forfeiture of
office seems like the most obvious.>
I was thinking that the random ballot outcome can be quite bad. E.g. the
expected scores in the two-sided pizza election:
6 pepperoni voters: 7.0
2 anchovy voters: 3.4
2 mushroom voters: 1.8
If someone blinks (e.g. an anchovy voter mistakenly doesn't set mushroom
as the consensus option), then the outcome is not particularly good for
society as a whole. All we really need is the expectation of the
lottery to be less than the consensus option, while resisting strategy.
So in some ideal world, the expected value for the fair lottery would be
something along the lines of
6 pepperoni voters: 8 - epsilon
2 anchovy voters: 8 - epsilon
2 mushroom voters: 9 - epsilon
and even for very small epsilon, it would still be preferable to choose
the mushroom consensus option. But how to implement such a lottery, much
less in a strategy-resistant manner, I have no idea.
In a way, it's like the concept of MAD: if you give every voter his
personal doomsday button to push if he doesn't get a satisfactory
outcome, then minmax will happen if it's at all achievable. However, the
outcome should consensus be impossible is truly horrible. The better the
system can be in the "no consensus" case while leaving consensus
preferable, the better the method is.
The other side of that coin is what I said in the earlier post: if the
consensus option is always at least as good as a random ballot, then
it'll always be chosen. So making the structure around the mechanism
conducive to finding a consensus would also help.
We'd have to be careful that the alternative to consensus isn't biased,
though. "Forfeiting one's office" might well be, just like "status quo
prevails" is.
Yes, you're right. There would at least need to be a clear cost to the participants for forfeiture of office to be an effective tool.
Kevin