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What is the best method to elect a prime minister or Speaker of the House?

 
 
 
B

Blahface

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Let's say you've got a legislature or another relatively small body (roughly around Dunbar's number) that needs to elect someone to some kind of position. This body is educated enough to know about any voting system and knows how to use their knowledge of their colleagues to come up with the best voting strategy to elect the candidate they like. What would the best voting system be to avoid strategic voting and ensure that the best candidate wins with very little chance of somebody accidentally winning due to a miscalculation of voting tactics?

I would use a Condorcet method that handles a cycle with a restricted version of range voting. Every member of this body would rank each candidate. They would then score each candidate with the following rules:

1) You can't score a candidate higher than a candidate you ranked higher.

2) The score given to a candidate must be at minimum (number of candidates- rank of candidate) multiplied by 3. For the first ranked candidate, this would also be the mandatory score and last place would have a mandatory score of 0 pts.

In a four candidate race, first place would get a score of 9 pts; second place could be 6 -9 pts; third place could be 3 to however many points the second candidate was scored. fourth place would get 0 points

If the UK used this system, do you think Nick Clegg would be Prime Minister instead of David Cameron?
 
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I think most politicians are corrupt. While voting for popularity is great for helping to stabalize government and reduce general unrest, I simply no longer trust people who have the craving to pursue power.

I would take a random sampling of maybe 5 individuals from the general population. These individuals would need to meet minimum standards of qualification. Within an appropriate age range, never diagnosed with a serious mental condition, never convicted of a felony.

The individuals would be asked to fill out a survey regarding their opinions and positions on a broad range of subjects and hypothetical situations. A short biography of the individual and a live TV interview/ debate posed with mostly softball questions would be all that the voting public would be allowed to know about the candidates.

After this, all voters must register two approval votes and three disapproval votes among the 5 standing candidates. Winner is the candidate with the most approval votes.
 
zorq said:
I think most politicians are corrupt. While voting for popularity is great for helping to stabalize government and reduce general unrest, I simply no longer trust people who have the craving to pursue power.

I would take a random sampling of maybe 5 individuals from the general population. These individuals would need to meet minimum standards of qualification. Within an appropriate age range, never diagnosed with a serious mental condition, never convicted of a felony.

The individuals would be asked to fill out a survey regarding their opinions and positions on a broad range of subjects and hypothetical situations. A short biography of the individual and a live TV interview/ debate posed with mostly softball questions would be all that the voting public would be allowed to know about the candidates.

After this, all voters must register two approval votes and three disapproval votes among the 5 standing candidates. Winner is the candidate with the most approval votes.
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I hate to derail my own thread, but I would increase the size of the group to maybe 225. I would put them together for a weekend assembly in which they would debate with each other and get a chance to talk to the candidates in person. You could also include representatives from different advocacy groups to argue their positions to the voters. The voters could randomly be assigned to smaller caucuses and from their caucuses they could debate each other and elect a caucus leader that would have time to put each candidate on the hot seat and ask them the tough questions in front of the assembly.
 
The way the legislative body itself is elected impacts the tactics they use. If the general election is first-past the post, very likely there would be two parliamentary blocs and the larger bloc would be able to appoint the prime minister no matter what the election system is. The real choice would be up to the party.

Now if there was some way to get legislature composed entirely of independents, then I suppose condorcet or IRV would do. But I think more important than the voting system is separation of powers. The candidates should not be members of the body that elects the PM, and in fact there should be a way to revise the results at any time if the electors change their minds. The PM should work for the legislature, rather than vice versa.
 
Jayjay said:
The way the legislative body itself is elected impacts the tactics they use. If the general election is first-past the post, very likely there would be two parliamentary blocs and the larger bloc would be able to appoint the prime minister no matter what the election system is. The real choice would be up to the party.

Now if there was some way to get legislature composed entirely of independents, then I suppose condorcet or IRV would do. But I think more important than the voting system is separation of powers. The candidates should not be members of the body that elects the PM, and in fact there should be a way to revise the results at any time if the electors change their minds. The PM should work for the legislature, rather than vice versa.
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With a Condorcet method, you wouldn't need too many independents to shake up the results. IRV would be more of a problem and it would not have an effect on most parliamentary systems.

As a safety valve for tactical voting gone wrong, you could make the winner of the election the default candidate unless the majority of the legislature decide to endorse a candidate they prefer within the next 24 hours. I'm afraid though that with this back up measure that some representatives will play chicken by helping to elect a really bad candidate and then say, "look, you've got to endorse my candidate. If you don't, this horrible candidate will get elected."
 
Blahface said:
I would use a Condorcet method that handles a cycle with a restricted version of range voting. Every member of this body would rank each candidate. They would then score each candidate with the following rules:

1) You can't score a candidate higher than a candidate you ranked higher.

2) The score given to a candidate must be at minimum (number of candidates- rank of candidate) multiplied by 3. For the first ranked candidate, this would also be the mandatory score and last place would have a mandatory score of 0 pts.

In a four candidate race, first place would get a score of 9 pts; second place could be 6 -9 pts; third place could be 3 to however many points the second candidate was scored. fourth place would get 0 points
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The difference that the scoring makes depends on the number of candidates. You can boost or lower the chances of any reasonably popular candidate that is not the favourite by manipulating the number of candidates, and manipulating how many candidates in each political grouping there are. That's why I prefer an STV based system to a score-based system.

Of course a lot depends on what you want to achieve. If you want to elect the candidate with the largest amount of solid supporters, rather than the least objectionable, then FPtP may be the way to go.
 
I like the random sampling and/or drafting ideas for office and I have some problems with political parties and think we should re-examine allowing them to exist.
 
Tigers! said:
I have some sympathy for the use of the Hare-Clark http://en.wikipedia.org/wiki/Single_transferable_vote
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I think STV would be the best way for representatives in congress to elect members to a committee.

I also think that it would be good to use it to proportionally ration out shares of time in congress’s schedule. Each week, there could be a list of potential items on the agenda that congress can vote on and rank.

There are things that congress should be able to do though without it being necessary to be on the schedule. Congress can discuss and debate on a public message-board, so you don't really need to set aside time for that unless you have someone from the outside giving expert testimony that congress needs to give followup questions to in real-time. You also don't really need to set aside time to vote on a bill. You could set a lifespan of a bill to maybe 60 days. Congress could vote any time to approve the bill or extend the lifespan of the bill. Once it gets majority approval it can move on to the other legislature or to the President to sign or veto.
 
Togo said:
Blahface said:
I would use a Condorcet method that handles a cycle with a restricted version of range voting. Every member of this body would rank each candidate. They would then score each candidate with the following rules:

1) You can't score a candidate higher than a candidate you ranked higher.

2) The score given to a candidate must be at minimum (number of candidates- rank of candidate) multiplied by 3. For the first ranked candidate, this would also be the mandatory score and last place would have a mandatory score of 0 pts.

In a four candidate race, first place would get a score of 9 pts; second place could be 6 -9 pts; third place could be 3 to however many points the second candidate was scored. fourth place would get 0 points
Click to expand...

The difference that the scoring makes depends on the number of candidates. You can boost or lower the chances of any reasonably popular candidate that is not the favourite by manipulating the number of candidates, and manipulating how many candidates in each political grouping there are. That's why I prefer an STV based system to a score-based system.

Of course a lot depends on what you want to achieve. If you want to elect the candidate with the largest amount of solid supporters, rather than the least objectionable, then FPtP may be the way to go.
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I would use STV for a multi-seat position such as I said in the last post to elect members of a committee. I would only use range voting as a tie breaker for when there is a Condorcet cycle ( A beats B: B beats C: C beats A). In some Condorcet methods it can become advantageous to vote tactically to purposefully create a cycle because the method of resolving the cycle might favor your candidate.

Btw, just to be clear, in this thread, I'm not talking about the best voting method in general. I'm talking about the best voting method in a situation in which you have a small group of people who are voting, understand the voting system very well, and have a good idea how their colleagues would vote so they have a great opportunity to exploit holes in the system and vote insincerely to give their candidate an edge.
 
Whatever system you use, if you have corrupt people voting and/or corrupt people counting the ballots, the result can still be gamed. The problem is not in the voting method. It is in the people who got there in the first place. The method they use to divide up the spoils is immaterial. Who gets what is always a foregone conclusion unless it is a Democrat who cheats on his wife.
 
arkirk said:
Whatever system you use, if you have corrupt people voting and/or corrupt people counting the ballots, the result can still be gamed. The problem is not in the voting method. It is in the people who got there in the first place. The method they use to divide up the spoils is immaterial. Who gets what is always a foregone conclusion unless it is a Democrat who cheats on his wife.
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I seem to recall that Stalin was once quoted saying that it doesn't matter how the vote went it is how it is counted that matters.
 
There are several methods for resolving cycles in Cordorcet methods, methods that do not require any additional information like candidate ratings. Here are some.

Definitions:
nc is the number of candidates
d(x,y) is the number of voters who prefer candidate x over candidate y.

The Schulze beatpath method. A path from candidate x to candidate y is a series of candidates c(i) where c(1) = x and c(n) = y and d(c(i),c(i+1)) > d(c(i+1),c(i)). The path's strength is the minimum value of d(c(i),c(i+1)) along the way. Let p(x,y) be the strength of the strongest path from x to y, and if there is no path, then it is zero.

The winner is candidate x such that p(x,y) > p(y,x) for all other candidates y. The next ones in line can be found by doing this comparison while omitting the ones before. The p's, unlike the d's, have no cycles.

One can calculate the path strengths using a variant of the Floyd–Warshall algorithm. It has run time O(nc3).

for candidate x:
_ for candidate y:
_ _ if y != x:
_ _ _ if d(x,y) > d(y,x):
_ _ _ _ p(x,y) = d(x,y)
_ _ _ else:
_ _ _ _ p(x,y) = 0

for candidate x:
_ for candidate y:
_ _ if y != x:
_ _ _ for candidate z:
_ _ _ _ if z != x and z != y:
_ _ _ _ _ p(y,z) = max(p(y,z), min(p(y,x), p(x,z)))

The minimax method. For each candidate x, find the maximum of score(y,x) for other candidates y. Sort them in reverse order, minimum first. The winner is the first one. There are three possible ways of calculating the score.

Winning votes: score(x,y) = if d(x,y) > d(y,x) then d(x,y) else 0
Margins: score(x,y) = d(x,y) - d(y,x)
Pairwise opposition: score(x,y) = d(x,y)

Its run time is O(nc2).

The Kemeny-Young method. Find all possible orderings of the candidates. Then for each ordering, add up d(x,y), where x is before y in the ordering. The winning ordering is the one with the largest sum.

Its run time is O(nc!)

The Tideman ranked-pairs method. Like the Kemeny-Young method, but greedy. Construct ordered pairs of all the candidates (x,y) where y != x. Sort them in reverse order by their values of d(x,y), greatest to least. Set a list L of the pairs to the empty list. Go down the sorted list of pairs P and do the following:

Create new list L' = L + P and check to see if it has any cycles. If it has none, then L = L', otherwise, L is unchanged.

When done, find the ordering of the candidates from the pairs in L. The candidate that's only a first member of a pair is the winner.

One can look for cycles with this algorithm. For every candidate, count how many first members of pairs it is, and also second members. Repeat until the list of pairs does not change:

Remove every candidate that has zero first members, zero second members, or both.
Remove every pair that contains a removed candidate.

If no pairs remain at the end, then the original pairs contained no cycles.

Run time: about O(nc4)

Copeland's method. Order the candidate by (number of pairwise victories) - (number of pairwise defeats). The winner is the top one.

Run time: O(nc2) (winner only), O(nc2*log(nc)) (full ordering)

Baldwin's method. A cross between the Borda count and instant runoff voting. In each round, do the Borda count on the remaining candidates and remove the lowest-scoring candidate.

Run time: O(nc3)

Nanson's method. A variation on the previous method where one removes the candidates with the average Borda score or below it.

Run time: O(nc2*log(nc))

Dodgson's method. For each candidate, count how many swaps of candidates are necessary to make some candidate a Condorcet winner. That is, if it is x, then d(x,y) > d(y,x) for all other candidates y. The candidate with the fewest swaps needed is the overall winner. The candidates are swapped in the ballots. I don't know if anyone has tried to implement this method, but it has some theoretical interest.

Black's method. Look for a Condorcet winner. If there is none, then use the Borda count's winner.
 
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 Independence of clones criterion refers to what effect similar candidates have. Similar meaning having similar sorts of votes. There are three types of effects:
  • Spoiling: clones hurt each other
  • Teaming: clones help each other
  • Crowding: clones affect how other candidates turn out

Voting systems subject to each:
  • None: Approval/range, IRV/AV, Schulze, Tideman
  • Spoiling: FPTP, runoff, minimax, Kemeny-Young
  • Teaming: Borda, Copeland, Baldwin, Nanson
  • Crowding: Copeland

Any other criteria that I ought to examine?
 
lpetrich said:
There are several methods for resolving cycles in Cordorcet methods, methods that do not require any additional information like candidate ratings.
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Black's method is decent at nullifying strategic advantage of a Condorcet burial. The reason I wanted to break the Condorcet cycle with restricted range is because I wanted it to be a more flexible version of Black's method. I have no idea if it would make it better or worse though. Some day I am going to program a voting simulation so I can run every test imaginable, but I've got a lot of stuff to do before I get around to that.

Maybe, as a backup, you could just make the winner of the election the default winner and give 24 hours for the electing body to come up with a different winner if he/she has majority acceptance. The problem I see with that though is that it may encourage voting members of the body to try to elect a bad candidate in order to play a game a chicken. A member of the body can say, "If you don't agree to elect my guy, you are going to get this guy who is even worse."
 
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