[EM] (7) MJ better than IRV & MAM

Tue Aug 9 09:07:53 PDT 2016

On 08/09/2016 12:05 AM, steve bosworth wrote:
> Hi Kristofer and everyone,
>
> ------------------------------------------------------------------------
>
> *From:*Kristofer Munsterhjelm <km_elmet at t-online.de>
> *Sent:* Saturday, August 6, 2016 3:16 PM
> *To:* steve bosworth; election-methods at lists.electorama.com
> *Subject:* Re: (5) MJ better than IRV & MAM
>
> On 07/20/2016 11:31 PM, steve bosworth wrote:
>> Hi Kristofer,

>>> Also, do you agree that MJ (like MAM) has the advantage over IRV in
>>> electing a single-winner only after counting all
>>> the votes of each voter (i.e. the ‘grades’ that every voter has given
>>> to all of the candidates)? In addition, I see MJ’s method of
>>> counting these grades as being easier for ordinary citizens to
>>> understand than MAM’s method.

>> Yes, MJ takes more information into account than IRV does, and its
>> decision is less chaotic, i.e. it makes better use of the information it
>> does take into account.

>>> Consequently, do you also prefer MJ to MAM?

>> In a scenario-2 situation, yes. In a scenario-3 situation, no.

> I think I may understand you here but to be sure, where did you
> previously describe ‘scenarios 2 & 3?

See my earlier reply "Re: (3) Kristofer and Steve on MJ & IRVa vs. MAM".

>>> I also see
>>> MJ as more likely to prompt voters not to ‘rank’ the candidates but
>>> instead to ‘grade’ all of them honestly, i.e. to encourage more voters
>>> to grade or REJECT each candidate in the light of each of their own
>>> visions of what an EXCELLENT, VERY GOOD, GOOD, ACCEPTABLE, or POOR
>>> candidate looks like.

>> What you're saying here is in essence that you think scenario 2 is more
>> likely to reflect the real world than scenario 3: that voters, if given
>> the opportunity to grade to a common standard, will do so. I suppose I
>> lean in that direction, but others (e.g. Kevin Venzke) disagree.
>>
>> If someone were to ask me "MJ or Condorcet?", I'd say "either is fine"
>> (assuming clone independent Condorcet etc).
>
> S:Do you see MAM as ‘independent Condorcet’?Is the Condorcet method you
> have in mind better than MAM?

MAM passes the independence of clones criterion, so yes, MAM is
clone-independent. See the same reply ("Re: (3)...") for the kind of 
criteria I'd like to have satisfied for the kind of Condorcet methods I 
prefer.

In essence, I'm saying it doesn't matter whether the Condorcet method 
is, say, MAM, River or Schulze. They all pass the criteria and so are 
all suitable. Perhaps I'd be slightly inclined towards River since it 
also passes IPDA, but the others are good too.

>> In the light of full
>> information, one might very well be better than the other, but as it is,
>> I don't know which direction it'd go.
>
> By ‘full information’, are you thinking of the seemingly impractical
> possibility of a strategic voter knowing in advance how all the other
> voters are planning to vote?

No, I mean if I, as a voting methods designer had full information of 
how the voters would behave under the different methods, then I would 
know which is better.

For instance, the question of whether the voters would exaggerate under 
MJ is a factual question, as is the question of whether the voters would 
perform the kind of massive strategy that would exclude ordinary 
Condorcet methods like MAM.

If I had full knowledge of the voters' behavior, I would know with 
certainty whether B&L's claim that voters can (and would) grade to a 
common standard instead of rank is true. The evidence they have gathered 
from Orsay suggests that it is; on the other hand, that evidence isn't 
complete proof because the voters could possibly change their behavior 
in a high stakes election, as Kevin said.

>>> In this connection, below your say with regard to MJ that ‘it seems more
>>> that voters value expressing their true preference, and as long as the
>>> benefit to strategy is less than what they gain by expressing their
>>> preference, honesty wins.’

>> Yes. There's a class of rating/grading methods that go like this:
>>
>> - Each voter gives information about each candidate (e.g. ratings,
>> grades). The information is so that if a candidate joins, that doesn't
>> need to change the information about any other candidate.
>> - The method works by calculating a score f(X) for each candidate X,
>> where the function only uses the information on that candidate alone.
>> - If a voter increases his grade or rating of some candidate X, f(X)
>> will never decrease.
>> - The candidate with the greatest f() score wins.
>>
>> In MJ, f returns the majority grade (possibly with some tiebreakers). In
>> Range, f returns the sum of ratings.
>
> Isn’t the ‘sum of ratings’ more manipulatable than majory-grades?

Yes, which is what I say later on. I am simply making a claim about a
group of methods, and showing that both MJ and Range are part of that class.

>> These methods all have the property that if a voter can cleanly separate
>> the candidates into two categories "I like these" and "I don't like
>> these", then he'll never be worse off by rating the former at maximum
>> and the latter at minimum.
>
> But he would not also be able to help elect the EXCELLENT candidate
> any more than the ACCEPTABLE candidate.

That is also true.

A problem with Range, in my view, is that there's a pretty strong
incentive to vote Approval-style (maximum and minimum only) to get the
most out of your ballot. But voting Approval-style can be risky in close
races.

Because both Range and MJ are part of the class above, some may argue
that the incentive exists in MJ as well. This depends on whether voters
will default to be honest or if you need an active deterrent against
strategy, because it takes a considerably larger mass of voters to shift
an MJ result than a Range result.

So what I am saying is that I think MJ goes clear of that problem, but I
can understand why others (like Kevin) don't.

>> I don't see mono-add-top or participation failures as being very
>> important. All-equal ballots irrelevance (IIB) is somewhat more
>> counterintuitive,

> Please explain: ‘All-equal ballots irrelevance (IIB)’

If a voter casts a ballot that rates or ranks every candidate equal,
then you'd expect the outcome (winner) to not change. If that is always 
the case for a particular system, then that system passes IIB, otherwise 
it does not.

That is, if it's ever possible for you to change who wins by casting
a ballot that ranks every candidate equal, then the method fails IIB.

In MJ, it's possible to have a ballot set where X wins, but if you add a 
ballot that grades every candidate equal, then Y wins instead.

>> However, again, I'd like to mention that this holds in a scenario-2
>> situation. If the voters start to use the grades as rankings (i.e. a
>> voter rating his first preference VERY GOOD, his second GOOD, his third
>> best ACCEPTABLE, and so on, even if he thinks every candidate is
>> mediocre), then much of the benefit of MJ is lost.
>
> I would rather say MJ would still retain the advantage of allowing
> each voter clearly to express her evaluations of each candidate, as well
> denying success to half of any such ranking manipulations.

In a pure ranking context, "Excellent" doesn't mean anything besides
"first choice", so there's no expression of evaluation. A pure-ranking 
voter would grade his first choice Excellent even if, in his opinion, 
the best candidate is a mediocrity.

>> If that happens, Condorcet methods are better.
>
> Given the above advantages of MJ which you acknowledge (e.g. its count
> being somewhat simpler for ordinary citizens to understand), and the
> fact that it, not Condorcet, escapes Arrow’s paradoxes. I would like to
> understand why you say ‘Condorcet methods are better’.Are not the
> rankings attached to Condorcet doubly subject to manipulation when
> compared to those that might be imported by some citizens using MJ to
> rank rather than grade?

It doesn't escape Arrow's paradox in a scenario-3/ranking setting.

Arrow's impossibility theorem says that you can't have all of unanimity,
non-dictatorship and independence of irrelevant alternatives (IIA).

IIA implies that if candidate X wins, then X should always win even if 
some of the other candidates had not been in the running.

However, when voters rank rather than grade, MJ fails IIA and thus is 
subject to Arrow's paradox. Here's an example of that:

25 voters: A excellent, B very good, C good
40 voters: B excellent, C very good, A good
35 voters: C excellent, A very good, B good

The MJ winner is C. Now suppose one of the losers, A, had not stood and 
the voters still were ranking instead of grading: they'd still call 
their first preferences excellent and second preferences very good and 
so on. Then the result would have been:

25 voters: B excellent, C very good
40 voters: B excellent, C very good
35 voters: C excellent, B very good

and B wins. So the elimination of A would change the winner from C to B.

In contrast, if the voters grade rather than rank, the elimination of A 
would give the following result:

25 voters:              B very good, C good
40 voters: B excellent, C very good
35 voters: C excellent,              B good

and C would still win.