Re: [EM] A design flaw in the electoral system
James, Juho and Fred, Thanks very much for looking at the argument. An individual vote has no effect on the formal outcome of the election; whether the vote is cast or not, the outcome is the same regardless. James Gilmour wrote: These statements worry me - surely they contain a logical flaw? If these statements were true and every elector responded rationally, no-one would ever vote. Then the outcome would not be the same. It's an interesting distinction, and it might help in answering a question I have about how people respond to this information (more on that below). But here I think you're looking at the effect of knowing (if indeed it is true) that a vote has no effect, whereas I'm looking at the effect of that vote itself. Maybe the easiest way to understand it is in retrospect, by looking at past votes that you cast. I make a statement concerning each of those votes and its actual effect in the objective world. Juho Laatu wrote: I think it is incorrect or at least misleading to say that individual votes do not have any influence. They do, as a group. If it had no bearing on the argument, then I might agree it's misleading to say it. But it's actually the premise of the argument. Yesterday I wrote to another correspondent: A more direct answer [how is it possible?] is in the rounding procedure that translates a fine-grained sum into a coarse-grained outcome (who gets into office). In that rounding, the effect of the fine grain is lost. ... Or, we might stand on empirical grounds and state: the measureable effect of an individual vote on the outcome is zero. Which raises another question, Why are people surprised to learn this? James's observation that no-one would ever vote if they accepted the truth of it might figure into the answer. But I think the fact itself is indisputable, a matter of empirical science. A simple thought experiment will demonstrate this: 1. Take the last election in which you voted, and look at its outcome (P). 2. Subtract your vote from that election. 3. Recalculate the outcome without your vote (Q). 4. Look at the difference between P and Q. 5. Repeat for all the elections you ever participated in. Your vote never made a difference. Most people feel uncomfortable or perplexed in this knowledge, and I think the feeling indicates that something's wrong. Fred Gohlke wrote: I am not entirely clear on the flow of logic in your abstract, but I get the sense that you're saying voters should be able to cast their vote and have it, too ... Voters are not pieces of cake. The act of voting does not remove their needs and desires from the political system. They should be able to continue to influence the political process after they've voted. I say that electors are physically separated from their ballots, and I explain why this procedure is necessarily a design flaw. I trace other flaws, faults and failures back to this (including the meaningless vote). But I say nothing about how to deal with the situation. I think we lack an understanding of the overall problem, so I'm just trying to figure it out. If I am offered options that affect my life, options that I've had no voice in defining, the ability to choose one of them is neither free nor democratic. On the contrary, it expresses my status as a subject of those who defined the options. The right to vote in such circumstances is a farce. Yet, I believe this too can be traced to the design flaw in the electoral system. It's surprising a single flaw could propagate so many failures, in such different forms, but it appears to be the case. This draft section (design flaw) dealt only with the flaw itself, and how it renders the results of the election technically invalid. Other sections (not yet drafted) will attempt to uncover the paths by which the design flaw propagates through society at large. -- Michael Allan Toronto, +1 416-699-9528 http://zelea.com/ James Gilmour wrote: Michael Allan Sent: Monday, October 03, 2011 9:31 AM ABSTRACT An individual vote has no effect on the formal outcome of the election; whether the vote is cast or not, the outcome is the same regardless. These statements worry me - surely they contain a logical flaw? If these statements were true and every elector responded rationally, no-one would ever vote. Then the outcome would not be the same. I am not into logic, but I suspect the flaw is in some disconnection between the individual and the aggregate. When A with 100 votes wins over B with 99 votes, we cannot say which of the 100 individual votes for A was the winning vote, but it is clear that is any one of those 100 votes had not been for A, then A would not have won. At best, if one A-voter had stayed at home, there would have been a tie. If one of the A-voters had voted for B instead, the outcome would have been very different. Or am
Re: [EM] Enhanced DMC
I like this. Regarding how approval is inferred, I'm also happy with Forest's
idea of using Range
(aka Score) type ballots (on which voters give their most preferred candidates
the highest numerical
scores) and interpreting any score above zero as approval and breaking approval
ties as any score
above 1 etc. Or any other sort of multi-slot ratings ballot where all except
the bottom-most slot is
interpreted as approval.
Another idea is to enter above-bottom equal-ranking between any 2 candidates in
the pairwise matrix
as a whole vote for both candidates, and then take each candidate X's highest
single pairwise score
as X's approval score.
Here are a couple of examples to demonstrate how this method varies from some
other Condorcet
methods.
48: A
01: AD
24: BD
27: CBD
D is the most approved candidate and in the Smith set, and so Smith//Approval
elects D.
Forest's Enhanced DMC or Covering DMC (and your suggested SARR
implementation)
elects B.
B covers D and to me looks like a better winner. This method has a weaker
truncation incentive
than Smith//Approval.
25: AB
27: BC
26: CA
22: C
Approvals: C75, B52, A51. AB 51-49, BC 52-48, CA 75-25
Plain DMC and using MinMax or one of the algorithms that is equivalent to it
when there are three
candidates (such as Schulze and Ranked Pairs and River) and weighing defeats
either by Winning
Votes or Margins all elect B.
If 5 of the 22 C voters change to A those methods all elect C (a failure of
Woodall's mono-sub-delete
criterion).
25: AB
27: BC
26: CA
17: C
05: A (was C)
Approvals: C70, A56, B52. AB 56-49, BC 52-48, CA 70-30.
In both cases our favoured method (like Smith//Approval) elects C, the
positionally dominant candidate. It
seems those other methods are more vulnerable to Push-over strategy.
(To be fair, Woodall has demonstrated that no Condorcet method can meet
mono-raise-delete.)
Chris Benham
From: Ted Stern araucaria.arauc...@gmail.com
To: election-methods@lists.electorama.com
Cc: Forest Simmons fsimm...@pcc.edu; Chris Benham cbenha...@yahoo.com.au
Sent: Wednesday, 5 October 2011 8:35 AM
Subject: Re: [EM] Enhanced DMC
After some private email exchanges with Forest and Chris, I'm
proposing a simple way of implementing Enhanced DMC, plus a new name,
Strong Approval Round Robin Voting (SARR Voting).
Ballot:
Ranked Voting, all explicitly ranked candidates considered approved.
Equal ranking allowed. I'm basing this on recommendation from Chris
Benham. I'm open to alternatives, but it seems to be the easiest way
to do it for now, and the most resistant to burying strategies.
Tallying:
Form the pairwise matrix, using the standard Condorcet procedure. In
the diagonal entries, save total Approval votes.
For N candidates, the list of candidates in order from highest to
lowest approval is
X_0, X_1, ..., X_k, X_{k+1}, ..., X_{N-1}
Initialize the Strong set to the empty set
Initialize the Weak set to the empty set.
For k = 0 to N-1,
If X_k is already in the Weak set, continue iterating. (X_k is
defeated by a higher approved candidate. This is called being
strongly defeated.)
If X_k loses to a member of the Weak set, continue iterating. (X_k
may defeat all higher approved candidates, but is weakly defeated
by at least one of them.)
If we're still here in the loop, X_k defeats all candidates in the
Strong Set and all candidates in the Weak set. (X_k covers all
previously added members of the Strong set.)
Add X_k to the Strong set and add all of X_k's defeats to the Weak
set.
Set the provisional winner to X_k.
The last provisional winner (the last candidate added to the Strong
set) is the winner of the election.
Note:
The first member of the Strong Set will be X_0.
It is easiest to do this by hand if you first permute the pairwise
array so that it follows the same X_0, ..., X_{N-1} ordering.
As an example election, consider the one on this page:
http://wiki.electorama.com/wiki/Marginal_Ranked_Approval_Voting
Iterating through E, A, C, B, D, we find
E: Strong and Weak Sets are empty, so E has no losses to either.
Strong set = {E}; Weak set = {C, D}
Provisional winner set to E.
A: A defeats Strong set {E} and Weak set {C, D}.
= Strong set = {E, A}; Weak set = {C, D}
Provisional winner set to A.
C: in Weak set, not added to Strong set.
B: Defeats A, but is defeated by D from Weak set (and is therefore
weakly defeated by A).
D: in Weak set, not added to Strong set.
A is the last candidate added to the Strong set, so A wins.
Ted
--
araucaria dot araucana at gmail dot com
On 26 Sep 2011 11:44:13 -0700, Chris Benham wrote:
Forest,
I think in general that if the approval scores are at all valid I
would go for the enhanced DMC winner over any of the chain building
methods we have considered. I think other considerations over-ride
the
