Majority
I am both a mathematician and a citizen. My main interest in the realm of
election methods is to understand the theoretical limitations of practical
election methods. Theory is supposed to be the servant of practice ... not
the other way around.
Election methods are tools of democracy. As such they have a
psycho/politico aspect that we neglect at our own peril.
What can we realistically expect from the voters? How do they want to
express their preferences? How do they expect their preferences to be
incorporated into a decision?
For starters, most voters believe in some form of "majority rule."
If there is a candidate A that is preferred by more than half of the voters
over any other candidate A', then (all else being equal) A rather than A'
should be elected.
The problem is that sometimes there is no such ideal majority pairwise
candidate IMPC. Who should be elected in that case?
Answer: How about the candidate closest to being such an IMPC?
How do you determine "closeness"?
Why not by how few additional ballots would suffice to convert a candidate
into an IMPC?
Is this too hard for citizens of a democracy to accept?
What objections might there be?
How to overcome reservations and persuade the electorate?
-Forest
Hi Forest,
For me, it would be necessary to "lock" the actually voted majorities in some way,
so that the thought experiment majorities don't override them and refute what they
stated.
Otherwise I think it's too spoiler-prone: If you're barely on the losing end of a
majority, but the majority was burdened with an additional candidate, then you
are more likely to win. You just need to squeak past the majority, while they need
far more additional votes to beat each other.
I would maybe form the CDTT (i.e. the Schwartz set resulting from replacing
non-majorities with ties) and only allow the thought experiment's winner to be a
candidate from the CDTT.
But this would still violate Plurality (and certainly lacks elegance).
Kevin
Le samedi 28 mai 2022, 13:59:47 UTC−5, Forest Simmons forest.simmons21@gmail.com a écrit :
I am both a mathematician and a citizen. My main interest in the realm of
election methods is to understand the theoretical limitations of practical
election methods. Theory is supposed to be the servant of practice ... not
the other way around.
Election methods are tools of democracy. As such they have a
psycho/politico aspect that we neglect at our own peril.
What can we realistically expect from the voters? How do they want to
express their preferences? How do they expect their preferences to be
incorporated into a decision?
For starters, most voters believe in some form of "majority rule."
If there is a candidate A that is preferred by more than half of the voters
over any other candidate A', then (all else being equal) A rather than A'
should be elected.
The problem is that sometimes there is no such ideal majority pairwise
candidate IMPC. Who should be elected in that case?
Answer: How about the candidate closest to being such an IMPC?
How do you determine "closeness"?
Why not by how few additional ballots would suffice to convert a candidate
into an IMPC?
Is this too hard for citizens of a democracy to accept?
What objections might there be?
How to overcome reservations and persuade the electorate?
-Forest
I'm confused... I thought Forest was providing a philosophical argument
in favour of minimax, but I can't read Kevin's reply as expressing
philosophical doubts over that method.
As for philosophy... I think it's important that the average voter
should be able to see that the electoral system is a fair way of
identifying a collective preference, but too much to ask for that he or
she should recognise it as the best way. The former needs a
philosophical argument similar to Forest's (understood as referring to
minimax).
CJC
On 29/05/2022 18:07, Kevin Venzke wrote:
Hi Forest,
For me, it would be necessary to "lock" the actually voted majorities in some way,
so that the thought experiment majorities don't override them and refute what they
stated.
Otherwise I think it's too spoiler-prone: If you're barely on the losing end of a
majority, but the majority was burdened with an additional candidate, then you
are more likely to win. You just need to squeak past the majority, while they need
far more additional votes to beat each other.
I would maybe form the CDTT (i.e. the Schwartz set resulting from replacing
non-majorities with ties) and only allow the thought experiment's winner to be a
candidate from the CDTT.
But this would still violate Plurality (and certainly lacks elegance).
Kevin
Hi Colin/Forest,
Colin Champion wrote:
I'm confused... I thought Forest was providing a philosophical argument
in favour of minimax, but I can't read Kevin's reply as expressing
philosophical doubts over that method.
To me minimax is more of a framework than a method, so I would not have so many
doubts about that, but rather about the specific treatment I (somewhat incorrectly)
understood Forest to be suggesting.
It looks like Forest's intended method was what Woodall called "MinGS."
Indeed this does not violate Plurality. It also satisfies LNHelp, mono-raise, and
mono-add-top.
But not only is it not a Condorcet method, it doesn't ensure mutual majority even
with three candidates. So I think the spoiler concern is still relevant.
Kevin
On 29/05/2022 18:07, Kevin Venzke wrote:
For me, it would be necessary to "lock" the actually voted majorities in some way,
so that the thought experiment majorities don't override them and refute what they
stated.
Otherwise I think it's too spoiler-prone: If you're barely on the losing end of a
majority, but the majority was burdened with an additional candidate, then you
are more likely to win. You just need to squeak past the majority, while they need
far more additional votes to beat each other.
I would maybe form the CDTT (i.e. the Schwartz set resulting from replacing
non-majorities with ties) and only allow the thought experiment's winner to be a
candidate from the CDTT.
But this would still violate Plurality (and certainly lacks elegance).