[EM] Defeat strength, Winning Votes vs. Margins, what to do with equal-ranks on the ballot?

robert bristow-johnson rbj at audioimagination.com
Mon Jun 3 00:17:44 PDT 2019

I just thought of a good reason for why equal-ranked votes marked on an RCV ballot should not count for either candidate, even if simple Margins is used as Defeat Strength which, unlike Winning Votes, would be unaffected by whether equal ranks are counted for both or for neither
This is about selling an RCV method to legislators and the public for use in real governmental elections.  I've always been leaning toward Ranked-Pairs using Margins and even with Margins, equal ranks should count for neither candidate because of the possibility of the total of
Winning Votes + Losing Votes exceeding the number of voters or the number of ballots issued.  If a large proportion of the electorate had no opinion regarding TweedleDee vs. TweedleDum, but rank them above Satan (who is left unranked and tied for last place with anyone else unranked), it might
seem odd in the TweedleDee vs. TweedleDum pairing if the sum of WV+LV exceeded the number of people voting.
I dunno, in multiwinner FPTP elections, the number of votes cast (assuming each voter can cast as many votes as there are seats) can be as high as the number of seats times the
number of voters.  But it would look weird if, in a single-winner RCV race if the total number of votes in any pair runoff exceeds the number of voters.
So I think (given the 2 to 4 principles below and given the need for simplicity and transparency in tallying) that Tideman Ranked Pairs
using Margins is the best to sell to the public and policy makers. Any unranked candidate is tied for last place on a ballot.  Equal ranking allowed on the ballot, but counts for neither candidate equally ranked..  This doesn't mean that Schulze (Margins) is not better, but it's more
complicated and makes no difference for a Smith Set of 3 or less.  And I don't think there will ever be a Condorcet-compliant RCV election that will ever have more than 3 in the Smith Set.  I think having a Condorcet cycle at all will be extremely rare in the context of a governmental
It's possible that IRV-BTR, which is Condorcet compliant, might be easier to sell to policy makers that have already been supporting RCV using IRV.  But there are also IRV haters (that probably don't want any kinda RCV and will always conflate RCV with IRV), so I am not sure if
any association with IRV, that IRV-BTR is a better sell than Ranked Pairs.  The precinct summability can still be used to verify the Condocet Winner, but if there is no CW, the tallying of the election (and the decision regarding the winner) is done only at the central location as is the case
with IRV.
just my rambling.
r b-j

---------------------------- Original Message ----------------------------

Subject: Re: [EM] Defeat strength, Winning Votes vs. Margins, what to do with equal-ranks on the ballot?

From: "robert bristow-johnson" <rbj at audioimagination.com>

Date: Sun, June 2, 2019 12:10 am

To: "EM" <election-methods at lists.electorama.com>



> ---------------------------- Original Message ----------------------------

> Subject: Re: [EM] Defeat strength, Winning Votes vs. Margins, what to do with equal-ranks on the ballot?

> From: "Kevin Venzke" <stepjak at yahoo.fr>

> Date: Wed, May 29, 2019 9:54 pm

> To: "EM" <election-methods at lists.electorama.com>

> --------------------------------------------------------------------------




>> Hi Robert,

> Hi,

>> I know that you feel it's adequate that there is a probabilistic relationship between (x-y) and (x+y).  I think

>> the relationship to expect in reality is unclear. Consider that in real world experience major contests that

>> involve the strongest candidates and most of the voters are often close races, in which case (x-y) doesn't

>> predict (x+y) well at all.


> it seems to me that one would expect x-y to scale with x+y.  if the decisiveness (which is the name that i give the percent margin, (x-y)/(x+y) ) is about the nature of the individuals voting, not about their quantity) is unchanged with size, then x-y is expected to get bigger as x+y
> does.  if the decisiveness is the equal between two paired runoffs in RP or Schulze, which decision is more important to satisfy?  the one involving more voters weighing in or the pairing with fewer?  



> and [(x-y)/(x+y)] * (x+y)^2 = x^2 -y^2 is interesting and it on the way to Winning Votes (it's the L^2 distance norm and as p gets higher, the L^p norm more and more emphasizes the Winning Votes, making the Losing Votes less relevant).

> But my interest is in the most simplest, yet adequate

> multi-candidate, single-winner method that can be sold to lawmakers and the public.

> IRV and FPTP is inadequate.  The minimum fundamental adequacy is, in my opinion:



> 1. One-person, one-vote.  Whether you prefer your candidate with much greater fervor than my preference for my candidate must not matter.  Our votes must count equally.

> 2. Majority preference prevails.  If more voters mark their ballots that Candidate A is preferred over

> Candidate B than the number of voters marking their ballots to the contrary, then Candidate B is not elected.

> Also important to me is:

> 3. Decisive on Election Day.  The election should be resolved, without additional voting, the moment all of the ballots marked are known (by the

> central counting computer).  Delayed runoffs are decided by half as many people that participated in the original election.

> 4. Precinct summability for a check on any nefarious election meddling at the central counting computer.



>> Personally I would say that (x-y) just reveals the lowest possible value for (x+y).

> No, i think that, if statistics are generated from actual elections you'll find (assuming x>y) that x-y will correlate with x+y.  The expectation value of x-y will increase with x+y .  I think

> viewing it as a binary probability distribution where the probability that a random voter votes for candidate X is x/(x+y) and the probability this randomly chosen voter votes for candidate Y is y/(x+y).  In this group I am leaving out the voters that preferred neither X nor Y. 


>> Your arguments about balancing decisiveness and size/salience are unique I think.

> Well, thank you, I think.  :-)

> It just seemed to me to be a natural or serendipitous reason that simple margin, x-y, is a good and simple measure of defeat strength of an election to compare to

> the defeat strength of other elections.

> I just think that Margins should be more mainline than WV or LV, which seem a little fringey to me.

>> I think it's more common to argue that salience is irrelevant or imaginary.

> Given the same decisiveness of the two elections, why

> should a smaller election count more than a larger election.  there are people disappointed with the result of any election.  the idea of majority rule is to reduce the number of disappointed persons with franchise.  assuming all voters have equal franchise, the net number of
> being disappointed are the Winning votes minus Losing Votes.  If we want to minimize that, we emphasize the results of elections with larger margins over those of smaller margins.

>> One issue in particular is that margins is supposed to incentivize voters to cast strict

>> rankings. If this works, then every contest will have about the same salience anyway.

> yes.  i would expect that. 

> regards,

> robert


r b-j                         rbj at audioimagination.com

"Imagination is more important than knowledge."

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