Electing Cabinets/Executive Committees
I assume there's methods for this, but I don't know the search terms: say I
want to proportionally elect an inhomogeneous committee, like a Cabinet or
a set of executive officers. What methods handle this?
On 2024-03-06 04:26, Closed Limelike Curves wrote:
I assume there's methods for this, but I don't know the search terms:
say I want to proportionally elect an inhomogeneous committee, like a
Cabinet or a set of executive officers. What methods handle this?
Steven Brams considers this exact problem in the book "Mathematics and
Democracy" (Chapter 9, "Allocating Cabinet Ministries in a Parliament").
He first gives the following algorithm:
For i = 1...n:
- Let the "current party" be the party next in line according to
Sainte-Laguë based on votes in the most recent parliamentary election.[1]
- Ask the current party which of the remaining positions it would like
to claim (e.g. PM, minister of defense, etc.)
- Assign the chosen position to the party.
He then shows that this method, although proportional, is nonmonotone in
the sense that sometimes a party might want to be asked later. So he
introduces a "trading step" where at each i, the current party may ask
some other party if it wants to go first instead. He finally shows that
this does not completely eliminate tactical voting problems, but that
"some of the problems of cabinet selection can be ameliorated if not
solved" (section 9.8).
If you don't have parties, you might want to look into the matrix vote:
https://en.wikipedia.org/wiki/Matrix_vote. I'm not aware of any
generalization to methods other than Borda; the obvious multi-way Range
method[2] is not proportional.
-km
[1] Section 9.3. discusses the different divisor methods, and Brams
argues that whether you'd prefer D'Hondt or Sainte-Laguë is a matter of
preference - whether you think large-party bias is worth it for
stability or not. IMHO, the way to solve kingmaker problems with party
list parliamentarism is to use a slightly consensus-biased ranked
method. If that method is house monotone, then it could be used as a
replacement here. (Note that this is not the same as using D'Hondt, due
to parallels to center squeeze if only first preferences are used.)
[2] Each voter rates each candidate for each position, then the method
selects candidates so that the sum of chosen candidate-position pairs is
maximized. This can be done by linear programming.
Very helpful, thank you! I'll try and see if there's anything from the fair
division or cake-cutting literature on this.
On Wed, Mar 6, 2024 at 3:01 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:
On 2024-03-06 04:26, Closed Limelike Curves wrote:
I assume there's methods for this, but I don't know the search terms:
say I want to proportionally elect an inhomogeneous committee, like a
Cabinet or a set of executive officers. What methods handle this?
Steven Brams considers this exact problem in the book "Mathematics and
Democracy" (Chapter 9, "Allocating Cabinet Ministries in a Parliament").
He first gives the following algorithm:
For i = 1...n:
- Let the "current party" be the party next in line according to
Sainte-Laguë based on votes in the most recent parliamentary election.[1]
- Ask the current party which of the remaining positions it would
like
to claim (e.g. PM, minister of defense, etc.)
- Assign the chosen position to the party.
He then shows that this method, although proportional, is nonmonotone in
the sense that sometimes a party might want to be asked later. So he
introduces a "trading step" where at each i, the current party may ask
some other party if it wants to go first instead. He finally shows that
this does not completely eliminate tactical voting problems, but that
"some of the problems of cabinet selection can be ameliorated if not
solved" (section 9.8).
If you don't have parties, you might want to look into the matrix vote:
https://en.wikipedia.org/wiki/Matrix_vote. I'm not aware of any
generalization to methods other than Borda; the obvious multi-way Range
method[2] is not proportional.
-km
[1] Section 9.3. discusses the different divisor methods, and Brams
argues that whether you'd prefer D'Hondt or Sainte-Laguë is a matter of
preference - whether you think large-party bias is worth it for
stability or not. IMHO, the way to solve kingmaker problems with party
list parliamentarism is to use a slightly consensus-biased ranked
method. If that method is house monotone, then it could be used as a
replacement here. (Note that this is not the same as using D'Hondt, due
to parallels to center squeeze if only first preferences are used.)
[2] Each voter rates each candidate for each position, then the method
selects candidates so that the sum of chosen candidate-position pairs is
maximized. This can be done by linear programming.
Just realized: for legislatures or orgs with proportional budgeting, this
can be done by VCG mechanism! Legislators "pay" for cabinet positions using
their share of the budget. Those who spend more voting power on cabinet
picks will have less voting power when it comes time to pass a budget.
(Downside: this is definitely complicated, even if it's probably a big
improvement in terms of efficiency.)
On Thu, Mar 7, 2024 at 8:00 AM Closed Limelike Curves <
closed.limelike.curves@gmail.com> wrote:
Very helpful, thank you! I'll try and see if there's anything from the
fair division or cake-cutting literature on this.
On Wed, Mar 6, 2024 at 3:01 AM Kristofer Munsterhjelm <
km_elmet@t-online.de> wrote:
On 2024-03-06 04:26, Closed Limelike Curves wrote:
I assume there's methods for this, but I don't know the search terms:
say I want to proportionally elect an inhomogeneous committee, like a
Cabinet or a set of executive officers. What methods handle this?
Steven Brams considers this exact problem in the book "Mathematics and
Democracy" (Chapter 9, "Allocating Cabinet Ministries in a Parliament").
He first gives the following algorithm:
For i = 1...n:
- Let the "current party" be the party next in line according to
Sainte-Laguë based on votes in the most recent parliamentary election.[1]
- Ask the current party which of the remaining positions it would
like
to claim (e.g. PM, minister of defense, etc.)
- Assign the chosen position to the party.
He then shows that this method, although proportional, is nonmonotone in
the sense that sometimes a party might want to be asked later. So he
introduces a "trading step" where at each i, the current party may ask
some other party if it wants to go first instead. He finally shows that
this does not completely eliminate tactical voting problems, but that
"some of the problems of cabinet selection can be ameliorated if not
solved" (section 9.8).
If you don't have parties, you might want to look into the matrix vote:
https://en.wikipedia.org/wiki/Matrix_vote. I'm not aware of any
generalization to methods other than Borda; the obvious multi-way Range
method[2] is not proportional.
-km
[1] Section 9.3. discusses the different divisor methods, and Brams
argues that whether you'd prefer D'Hondt or Sainte-Laguë is a matter of
preference - whether you think large-party bias is worth it for
stability or not. IMHO, the way to solve kingmaker problems with party
list parliamentarism is to use a slightly consensus-biased ranked
method. If that method is house monotone, then it could be used as a
replacement here. (Note that this is not the same as using D'Hondt, due
to parallels to center squeeze if only first preferences are used.)
[2] Each voter rates each candidate for each position, then the method
selects candidates so that the sum of chosen candidate-position pairs is
maximized. This can be done by linear programming.
See https://en.wikipedia.org/wiki/Method_of_Equal_Shares
and its associated website, https://equalshares.net/
On Mon, Mar 11, 2024 at 10:23 AM Closed Limelike Curves <
closed.limelike.curves@gmail.com> wrote:
Just realized: for legislatures or orgs with proportional budgeting, this
can be done by VCG mechanism! Legislators "pay" for cabinet positions using
their share of the budget. Those who spend more voting power on cabinet
picks will have less voting power when it comes time to pass a budget.
(Downside: this is definitely complicated, even if it's probably a big
improvement in terms of efficiency.)
On Thu, Mar 7, 2024 at 8:00 AM Closed Limelike Curves <
closed.limelike.curves@gmail.com> wrote:
Very helpful, thank you! I'll try and see if there's anything from the
fair division or cake-cutting literature on this.
On Wed, Mar 6, 2024 at 3:01 AM Kristofer Munsterhjelm <
km_elmet@t-online.de> wrote:
On 2024-03-06 04:26, Closed Limelike Curves wrote:
I assume there's methods for this, but I don't know the search terms:
say I want to proportionally elect an inhomogeneous committee, like a
Cabinet or a set of executive officers. What methods handle this?
Steven Brams considers this exact problem in the book "Mathematics and
Democracy" (Chapter 9, "Allocating Cabinet Ministries in a Parliament").
He first gives the following algorithm:
For i = 1...n:
- Let the "current party" be the party next in line according to
Sainte-Laguë based on votes in the most recent parliamentary election.[1]
- Ask the current party which of the remaining positions it
would like
to claim (e.g. PM, minister of defense, etc.)
- Assign the chosen position to the party.
He then shows that this method, although proportional, is nonmonotone in
the sense that sometimes a party might want to be asked later. So he
introduces a "trading step" where at each i, the current party may ask
some other party if it wants to go first instead. He finally shows that
this does not completely eliminate tactical voting problems, but that
"some of the problems of cabinet selection can be ameliorated if not
solved" (section 9.8).
If you don't have parties, you might want to look into the matrix vote:
https://en.wikipedia.org/wiki/Matrix_vote. I'm not aware of any
generalization to methods other than Borda; the obvious multi-way Range
method[2] is not proportional.
-km
[1] Section 9.3. discusses the different divisor methods, and Brams
argues that whether you'd prefer D'Hondt or Sainte-Laguë is a matter of
preference - whether you think large-party bias is worth it for
stability or not. IMHO, the way to solve kingmaker problems with party
list parliamentarism is to use a slightly consensus-biased ranked
method. If that method is house monotone, then it could be used as a
replacement here. (Note that this is not the same as using D'Hondt, due
to parallels to center squeeze if only first preferences are used.)
[2] Each voter rates each candidate for each position, then the method
selects candidates so that the sum of chosen candidate-position pairs is
maximized. This can be done by linear programming.
Election-Methods mailing list - see https://electorama.com/em for list
info
On 3/5/2024 7:26 PM, Closed Limelike Curves wrote:
I assume there's methods for this, but I don't know the search terms:
say I want to proportionally elect an inhomogeneous committee, like a
Cabinet or a set of executive officers. What methods handle this?
Here's a calculation method I designed, applied to an example in which
the winners are cabinet ministers:
http://www.negotiationtool.com/cabinetministers.html
The calculation code is on GitHub, with the ReadMe being here:
https://github.com/cpsolver/VoteFair-Negotiation-Tool/blob/master/README
There's one paragraph about it on ElectoWiki here, under "VoteFair Ranking":
https://electowiki.org/wiki/VoteFair_Ranking
I just found your question in a junk/spam folder, hence the delay in
replying.
Richard Fobes
The VoteFair guy
On 3/5/2024 7:26 PM, Closed Limelike Curves wrote:
I assume there's methods for this, but I don't know the search terms:
say I want to proportionally elect an inhomogeneous committee, like a
Cabinet or a set of executive officers. What methods handle this?
Election-Methods mailing list - see https://electorama.com/em for list info
I also have not seen this question before, and am not sure who wants to
know the answer, tho I think all election methodologists should know
that a general election method is sought that applies to all election
circumstances (not to mention data representation in general).
Obviously a proportional election requires a proportional count, and
what should be obvious, a preference vote, by which the voters can
convey that proportional count. At least the mathematician Carl Andrae
thought it was obvious when he invented the method in the 1850s. The key
to understanding the Andrae system (Hare system, In English-speaking
countries) is that you don't do what politicians did to the Andrae
system, which was to shut voters into dogmatic little boxes, labeled
this party or that. Because choice is relative, a question of more or
less, as is proved by the concepts of a "wasted vote" (ever used by big
parties twisting the arms of smaller parties supporters) and "strategic"
or "tactical voting" (ever used by small parties trying to gain on
bigger parties).
The term "inhomogenous" implicitly (maybe not intentionally)
disqualifies the partisan ideal, which assumes voters are dogmatic
supporters of one party, and to represent as many, or as few, as
possible, the election method just regulates the election threshold.
This, however, over-looks cross-party sympathies, meaning that people
may be sensible, to some extent, to the virtues and vices of more then
one party. To recognise this reality of cross-party proportional
representation, as well as party proportional representation requires a
transferable vote, both for independents outside parties, as well as
independence within parties. I mean so that representatives, are
directly accountable to the voters, as they are meant to be in a
democracy, and not to party bosses, as is the case with party list
systems. (Millions of people, thru-out the English-speaking world use
non-partisan PR/STV, which really answers the question on this list.)
The logical details, that so absorb methodologists, are adequately
over-come by at-large elections with STV. This is because as the
election becomes more and more proportonal with more seats per
constituency, the residual crude "last past the post" exclusion count
becomes less and less important in determining the result. Indeed
Instant Run-off Voting in single member districts is an irrational
exclusion count rather than an election. It is the necessary reform of
the vote, without an implied proportional reform of the count. The
purpose of a preference vote is not to eliminate preferences but to
elect proportions.
These detailed problems with traditional STV can be over-come. It is
possible to have a rational exclusion count, as well as a rational
election count. That is the system I have developed with Binomial STV.
This is a consistent one-truth count not an inconsistent two (or more)
truths count by conventional voting methods in general.
Regards,
Richard Lung.
On 29/03/2024 22:10, Richard, the VoteFair guy wrote:
On 3/5/2024 7:26 PM, Closed Limelike Curves wrote:
I assume there's methods for this, but I don't know the search terms:
say I want to proportionally elect an inhomogeneous committee, like a
Cabinet or a set of executive officers. What methods handle this?
Here's a calculation method I designed, applied to an example in which
the winners are cabinet ministers:
http://www.negotiationtool.com/cabinetministers.html
The calculation code is on GitHub, with the ReadMe being here:
https://github.com/cpsolver/VoteFair-Negotiation-Tool/blob/master/README
There's one paragraph about it on ElectoWiki here, under "VoteFair
Ranking":
https://electowiki.org/wiki/VoteFair_Ranking
I just found your question in a junk/spam folder, hence the delay in
replying.
Richard Fobes
The VoteFair guy
On 3/5/2024 7:26 PM, Closed Limelike Curves wrote:
I assume there's methods for this, but I don't know the search terms:
say I want to proportionally elect an inhomogeneous committee, like a
Cabinet or a set of executive officers. What methods handle this?
Election-Methods mailing list - see https://electorama.com/em for
list info
Election-Methods mailing list - see https://electorama.com/em for list
info
Perhaps this improvement would make the algorithm monotone:
- Calculate the proportional ranking, but start assigning ministries from the
last place, not the first one. - When a party/candidate chooses a ministry, they can choose either from
among the not selected ones or the ones selected by someone in a lower
place. - If a new ministry was chosen, it's the next higher place's turn.
- If a previously chosen ministry was chosen again, the lower place loses
the ministry and it is now their turn to choose.
Of course the backtracking can happen automatically if the participating
parties just state their preferred ministries instead of making
turn-by-turn choices.
śr., 6 mar 2024 o 12:01 Kristofer Munsterhjelm km_elmet@t-online.de
napisał(a):
On 2024-03-06 04:26, Closed Limelike Curves wrote:
I assume there's methods for this, but I don't know the search terms:
say I want to proportionally elect an inhomogeneous committee, like a
Cabinet or a set of executive officers. What methods handle this?
Steven Brams considers this exact problem in the book "Mathematics and
Democracy" (Chapter 9, "Allocating Cabinet Ministries in a Parliament").
He first gives the following algorithm:
For i = 1...n:
- Let the "current party" be the party next in line according to
Sainte-Laguë based on votes in the most recent parliamentary election.[1]
- Ask the current party which of the remaining positions it would
like
to claim (e.g. PM, minister of defense, etc.)
- Assign the chosen position to the party.
He then shows that this method, although proportional, is nonmonotone in
the sense that sometimes a party might want to be asked later. So he
introduces a "trading step" where at each i, the current party may ask
some other party if it wants to go first instead. He finally shows that
this does not completely eliminate tactical voting problems, but that
"some of the problems of cabinet selection can be ameliorated if not
solved" (section 9.8).
If you don't have parties, you might want to look into the matrix vote:
https://en.wikipedia.org/wiki/Matrix_vote. I'm not aware of any
generalization to methods other than Borda; the obvious multi-way Range
method[2] is not proportional.
-km
[1] Section 9.3. discusses the different divisor methods, and Brams
argues that whether you'd prefer D'Hondt or Sainte-Laguë is a matter of
preference - whether you think large-party bias is worth it for
stability or not. IMHO, the way to solve kingmaker problems with party
list parliamentarism is to use a slightly consensus-biased ranked
method. If that method is house monotone, then it could be used as a
replacement here. (Note that this is not the same as using D'Hondt, due
to parallels to center squeeze if only first preferences are used.)
[2] Each voter rates each candidate for each position, then the method
selects candidates so that the sum of chosen candidate-position pairs is
maximized. This can be done by linear programming.
Election-Methods mailing list - see https://electorama.com/em for list
info