<div dir="ltr"><div class="gmail_quote"><div dir="ltr"><div class="gmail_extra"><br><div class="gmail_quote"><span class="">2016-09-17 0:42 GMT-04:00 C.Benham <span dir="ltr"><<a href="mailto:cbenham@adam.com.au" target="_blank">cbenham@adam.com.au</a>></span>:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div bgcolor="#FFFFFF">
<div><span>On 9/16/2016 4:22 AM, steve bosworth
wrote:<br>
<blockquote type="cite"><span style="line-height:107%;font-size:12pt"><font face="Calibri">MJ simply asks each voter to grade
each candidate when judged against each voter’s own criteria
of what an EXCELLENT candidate would look like.<span>
</span>Any candidate judged to be less than EXCELLENT must
be graded either as VERRY GOOD, GOOD, ACCEPTABLE, POOR, or
REJECTED.<span>
</span>Balinski and Laraki refer to each voters own criteria
for grading candidates as being ‘absolute’ (but this is only
in the sense that these criteria should be independent of
any one set of candidates that might be seeking election).<span> </span></font></span></blockquote>
<br></span>
C: To begin with superficial aesthetics, the grades should have
simple neutral names (like A B C D E F) and the ballot "request"
should be something like:<br>
"Give your favourite candidate or candidates an A and and your
least preferred candidate or candidates an F and any intermediate
candidates whatever<br>
grade you see fit. Default rating is F."<br>
<br>
As it is if in a given election A , by my "criteria that should
be independent of any one set of candidates that might be seeking
election" , such as those doing so in election A,<br>
I rate my favourite candidate as being merely "Acceptable" I
would resent having to either (a) accept that my vote will have
less influence on the result than voters who rate<br>
their favourite as "Excellent" or (b) "lie" and falsely indicate
that I rate my favourite as "Excellent".<br></div></div></blockquote><div><br></div></span><div>To me, this parses as either an overgeneralization or a misapprehension of how MJ works.<br></div><div><br></div><div>But before I get to my strongest criticism in that regard, let me discuss why I feel the issue is less important than one might thing. Saying that the criteria should be "independent of any one set of candidates that might be seeking election" does not mean that it should be "independent of the population distribution of candidates that typically seek such elections, weighted by win probability". A reasonable calibration for 5 ratings levels (ABCDF) and a metric under which that distribution is normal might put the cutoffs at something like +1.4, +.7, 0, -.7 standard distributions; or in other words, at the 90th, 75th, 50th, and 25th percentiles of historical winners and close second-place finishers.</div><div><br></div><div>Assuming that the distribution of people who run for an office is at least 1/3 wider than the distribution of those who can win it (reasonable) and that it's centered at the same place for our voter (probably not true for all, but a reasonable assumption in order to avoid pesky constants), then those cutoffs would be at about 83, 67, 50, and 33 percentiles of the full set of candidates. Assuming independence (which is an ABSOLUTELY unjustified worst-case assumption, purely for illustrative purposes), a 5-candidate race would have nobody at B or higher under 10% of the time. If you want to talk only viable (potentially-winning) candidates, that's still under 20%. So the case where a voter would have to be "dishonest" by two grade levels in order to use a full spectrum is unusual. </div><div><br></div><div>OK, now the real objection.</div><div><br></div><div>You say that anybody who honestly votes their favorite below top must "accept that [their] vote will have less influence on the result than voters who rate their favourite as "Excellent". But if their favorite candidate gets a median rating below the rating they give, then their honest vote is in fact fully strategic. Generally, given the calibration above, this will be the case with very high probability. In order to put specific numbers on that probability, I'd have to make a thicket of tenuous assumptions about how voter's candidate utilities distribute and correlate, so I won't do it, but I would be more surprised if the probability were under 90% than if it were over 95%.</div><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div bgcolor="#FFFFFF"><div><span class="">
<br>
MJ poses as being somewhat like a jury in a trial, or a panel
that judges say a competitive performance of Gymnastics or Diving.
<br>
<br>
But elections for powerful public political elections are very
different. In those cases the jurors/judges are more-or-less
"disinterested", i.e. it doesn't really make any<br>
possible difference to their lives who wins the competition or
whether the accused is jailed or set free. In elections who wins
the election could have a big effect on the<br>
lives of voters. <br>
<br>
Also in those other cases there is usually general agreement what
an excellent sporting performance looks like and what a terrible
sporting performance looks like and<br>
what constitutes clear proof of guilt or innocence. In elections
voters often have opposing ideologies, i.e. very different ideas
of what policies, priorities, political philosophy,<br>
diplomatic/military strategies the election winner should have.<br>
<br>
Another difference is that in those other cases the people on the
jury in a trial or the panel judging a sporting performance base
their decisions the same evidence. The jurors<br>
all hear the same evidence and arguments and base their verdict on
that. Likewise the judging panel all closely watch the same
performance and give their scores based purely<br>
on that.<br>
<br>
But voters in public elections vary widely in terms of what
information they get, and the quality and quantity of that
information. And of course much of the "information" they<br>
use might be false or misleading, generated by those with a big
interest in who wins the election.<br>
<br>
Leaving aside the strategy incentive for voters to only use the
very top and very bottom grades, suppose that all the voters rate
the candidates as sincerely as they can<br></span>
in the way MJ "invites" them to. Suppose that that there are
only two candidates with any hope of winning, X and Y. Suppose I (Chris) think that X is clearly better than Y<br>
and you (Jameson) think the opposite. Suppose my rating of X is B and of Y is D, and your rating of Y is A and of X is F.<span class=""><br>
<br>
Your pairwise preference will have greater weight than mine. </span></div></div></blockquote><div><br></div><div>No, it won't. Either they will both have equal weight (most probably), or Chris's vote will have no weight at all (improbable). There is no case where they will both have an impact but Jameson's impact will be greater.</div><div><br></div><div>First off, you yourself say you prefer letter grades over verbal categories. So I've edited your senario above to use corresponding letter grades, and to use X and Y for the candidate names.</div><div><br></div><div>So the hypothetical votes are:</div><div>Chris: X:B, Y:D</div><div>Jameson: X:F, Y:A</div><div><br></div><div>If the winning median is anything from B- to D+, then our votes had exactly the same impact. A winning median in this range is probable if people calibrate as I suggested above. And when it falls outside of that range, it will probably be predictable beforehand, giving Chris a chance to decide to be more strategic for one election only.</div><div><div class="h5"><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div bgcolor="#FFFFFF"><div>Is
that fair? According to the MJ philosophy your vote should have
greater weight because you are more<br>
"enthusiastic" in your support for B over A. Does this greater
enthusiasm mean that your opinion that B is better than A is more
likely to be correct than my opposite<br>
opinion?<span><br>
<br>
<blockquote type="cite"><span style="line-height:107%;font-size:12pt">Also, MJ seems to offer less scope for manipulative
voting than any other method.<span> </span></span></blockquote>
<br></span>
C: As Kevin has pointed out, sincere voters are less likely to be
at a disadvantage than with Range (aka Average Ratings) but in
both the voter's best strategy is to only<br>
use the two most extreme ratings. If all the voters do that the
method is just Approval.<br>
<br>
What exactly is your definition of "manipulative"?<span><br>
<br>
<blockquote type="cite"><span style="line-height:107%;font-size:12pt">I still favor MJ even though it is theoretically
vulnerable to ‘Later-no-harm’ (LNH).</span></blockquote>
<br></span>
C: I don't particularly care about Later-no-Harm. It encourages
the expression of preferences that may be very weak, and to the
extent that they are decisive they<br>
would tend to lower the "Social Utility" (SU) of the winner. And
the expressed preferences are also more likely to be the result of
unprincipled mutual back-scratching<br>
deals between candidates. <br>
<br>
I put a greater value on Later-no-Help (which MJ, along with MTA
and MCA meets). Ideally there should be weak zero-info truncation
incentive.<br>
<br>
But MJ has a very strong truncation incentive. It's compliance
with LNHelp is in practice useless if the voters should all
truncate.<br>
<br>
IRV meets both of Later-no-Help and Later-no-Harm, and in my
opinion it is the best of the methods that meet Later-no-Help.<br>
<br>
Other methods I like fail both. That is better than only meeting
LNHarm and so having a random-fill incentive, or only meeting
LNHelp and having a very<br>
strong truncation incentive.<br>
<br>
For reasons I might give in another post, I don't much like MAM.
A simpler Condorcet method I like is Smith//Approval:<br>
<br>
Voters ignore candidates they don't approve and rank the rest.
Equal-ranking allowed. Elect the most approved member of the
Smith set.<br>
<br>
The "Smith set" is the smallest set of candidate/s who all
pairwise beat all (if any) outside-the-set members. A
single-member "Smith set" is the <br>
Condorcet winner.<br>
<br>
Compliance with both FBC and Condorcet is impossible. MJ meets
FBC.<br>
<br>
A MJ-like method that is simpler and in my view better is
Majority Top Approval (MTA).<br>
<br>
It uses 3-slot ratings ballots. Default rating is Bottom. If any
candidate is rated above bottom on more than half the ballots,
elect (if there is more than one) the<br>
one of those with the highest number of top ratings. Otherwise
elect the candidate with the highest number of above-bottom
ratings.<br>
<br>
The voters' best strategy is to normally use only the top and
bottom ratings slots, but the middle slot is handy if there is one
or more candidate the voter is<br>
unsure how should rate on a 2-slot ratings ballot, or if the voter
is prepared to maybe take a small strategic risk for the sake of
being more expressive.<br>
<br>
But a more complex method I much prefer is IBIFA.<br>
<br>
<a href="http://wiki.electorama.com/wiki/IBIFA" target="_blank">http://wiki.electorama.com/wik<wbr>i/IBIFA</a><br>
<br>
Chris Benham<br>
<br>
<br>
</div>
<blockquote type="cite"><div><div>
<div style="font-size:14pt;color:rgb(0,0,0);font-family:calibri,arial,helvetica,sans-serif;background-color:rgb(255,255,255)">
<p style="margin:0in 0in 8pt"><span style="line-height:107%;font-size:12pt"><font face="Calibri"> </font></span></p>
<p style="margin:0in 0in 8pt"><span style="line-height:107%;font-size:12pt"><font face="Calibri"> </font></span></p>
<p style="margin:0in 0in 8pt"><span style="line-height:107%;font-size:12pt"><font face="Calibri"> </font></span></p>
<p style="margin:0in 0in 8pt"><span style="line-height:107%;font-size:12pt"><font face="Calibri">______________________________<wbr>__________</font></span></p>
<p style="margin:0in 0in 8pt"><span style="line-height:107%;font-size:12pt"><font face="Calibri">From: Kristofer
Munsterhjelm <a href="mailto:km_elmet@t-online.de" target="_blank"><km_elmet@t-online.de></a></font></span></p>
<p style="margin:0in 0in 8pt"><span style="line-height:107%;font-size:12pt"><font face="Calibri">Sent: Wednesday, June
1, 2016 9:14 PM</font></span></p>
<p style="margin:0in 0in 8pt"><span style="line-height:107%;font-size:12pt"><font face="Calibri">To: steve bosworth;
<a href="mailto:election-methods@lists.electorama.com" target="_blank">election-methods@lists.elector<wbr>ama.com</a></font></span></p>
<p style="margin:0in 0in 8pt"><span style="line-height:107%;font-size:12pt"><font face="Calibri">Subject: Re: [EM](6)
To Kristofer and everyone: MJ best to ‘tolerate’</font></span></p>
<p style="margin:0in 0in 8pt"><span style="line-height:107%;font-size:12pt"><font face="Calibri">______________________________<wbr>_____________</font></span></p>
<p style="margin:0in 0in 8pt"><span style="line-height:107%;font-size:12pt"><font face="Calibri"> </font></span></p>
<p style="margin:0in 0in 8pt"><span style="line-height:107%;font-size:12pt"><font face="Calibri">To Kristofer and
everyone:</font></span></p>
<p style="margin:0in 0in 8pt"><span style="line-height:107%;font-size:12pt"><font face="Calibri">Kristofer, while our
most recent exchange was on June 31<sup>st</sup>, I want
to thank you for forcing me to think more carefully and
completely.<span>
</span>As a result of the clarifications you offered me,
when combined with my recent EM discussions with Kevin and
Jameson, I am currently favoring MJ over all other methods
for electing a president.
</font></span></p>
<p style="margin:0in 0in 8pt"><span style="line-height:107%;font-size:12pt"><font face="Calibri">MJ simply asks each
voter to grade each candidate when judged against each
voter’s own criteria of what an EXCELLENT candidate would
look like.<span>
</span>Any candidate judged to be less than EXCELLENT must
be graded either as VERRY GOOD, GOOD, ACCEPTABLE, POOR, or
REJECTED.<span>
</span>Balinski and Laraki refer to each voters own
criteria for grading candidates as being ‘absolute’ (but
this is only in the sense that these criteria should be
independent of any one set of candidates that might be
seeking election).<span>
</span>These criteria are not rankings but they can be
used to make rankings.<span>
</span>MJ’s winner is the candidate whose majority
‘median-grade’ is higher than any other candidate.</font></span></p>
<p style="margin:0in 0in 8pt"><span style="line-height:107%;font-size:12pt"><font face="Calibri">For example, I see MJ
as both better than IRV and MJ because:
</font></span></p>
<ol style="list-style-type:decimal;direction:ltr">
<li style="color:rgb(0,0,0);font-size:12pt;font-style:normal;font-weight:normal">
<p style="color:rgb(0,0,0);font-size:11pt;font-style:normal;font-weight:normal;margin-top:12pt;margin-bottom:0pt">
<span style="line-height:107%;font-size:12pt">I
believe that ordinary citizens would more easily
understand both how to mark MJ’s ballot and how the
winner is discovered using its count.<span>
</span>They would find it even more difficulty in
understanding how MAM’s ballots are counted.
</span></p>
</li>
<li style="color:rgb(0,0,0);font-family:calibri,sans-serif;font-size:12pt;font-style:normal;font-weight:normal">
<p style="color:rgb(0,0,0);font-family:calibri,sans-serif;font-size:11pt;font-style:normal;font-weight:normal;margin-top:12pt;margin-bottom:0pt">
<span style="line-height:107%;font-size:12pt">At the
same time, both MJ and MAM have the following similar
advantage over IRV:<span>
</span>All MAM voters’ ‘rankings’ and MJ voters’
‘gradings’ of all candidates continue to count until
their respective winners are discovered.<span>
</span>Some of the IRV voters’ ‘rankings’ are not
counted after any of its candidates are eliminated and
before IRV’s winner is discovered.
</span></p>
</li>
<li style="color:rgb(0,0,0);font-family:calibri,sans-serif;font-size:12pt;font-style:normal;font-weight:normal">
<p style="color:rgb(0,0,0);font-family:calibri,sans-serif;font-size:11pt;font-style:normal;font-weight:normal;margin-top:12pt;margin-bottom:0pt">
<span style="line-height:107%;font-size:12pt">However,
MJ has another advantage over MAM: because ‘grades’ are
more evaluatively clear than are ‘ranks’, MJ’s ‘</span><span style="line-height:107%;font-size:12pt">‘majorities of grades are … considerably more
discerning decisions than are [MAM’s] majorities of
<span> </span>preferences’
(Belinski & Laraki, Majority Judgment, p.283)?
</span></p>
</li>
<li style="color:rgb(0,0,0);font-family:calibri,sans-serif;font-size:12pt;font-style:normal;font-weight:normal">
<p style="color:rgb(0,0,0);font-family:calibri,sans-serif;font-size:11pt;font-style:normal;font-weight:normal;margin-top:12pt;margin-bottom:0pt">
<span style="line-height:107%;font-size:12pt">Moreover,
unlike the different intensities of each MJ voter’s
‘grades’ (evaluations) for each candidate, the different
intensities of each MAM voter’s ‘rankings’ recorded on
her ballot are not directly counted.<span>
</span>For example, an MAM voter’s different intensities
of preference for A over B and A over G in the following
list of preferences are not differently counted:<span>
</span>A>B>C>D>E>F>G.<span> </span>In contrast, all
the ‘grades’ given to all candidates by all MJ voters
continue fully to count until the highest
‘majority-grade’ winner is discovered.
</span><span style="line-height:107%;font-size:12pt">T</span><span style="line-height:107%;font-size:12pt">hus, I see MJ as the most democratic
method because it both wastes no citizen’s vote and is
most likely to elect the candidate who is supported as
enthusiastically as possible by the larges majority of
citizens.</span></p>
</li>
<li style="color:rgb(0,0,0);font-family:calibri,sans-serif;font-size:12pt;font-style:normal;font-weight:normal">
<p style="color:rgb(0,0,0);font-family:calibri,sans-serif;font-size:11pt;font-style:normal;font-weight:normal;margin-top:12pt;margin-bottom:0pt">
<span style="line-height:107%;font-size:12pt">Also, MJ
seems to offer less scope for manipulative voting than
any other method.<span>
</span>B&L argue that MJ is entirely strategy-proof
with regard to grades.<span>
</span>At the same time, if B&L’s mathematical
proofs are correct, even when and if voters might
instead use MJ’s ‘gradings’ as ‘rankings’, MJ
structurally cuts by almost ‘half’</span><span style="line-height:107%;font-size:12pt">
</span><span style="line-height:107%;font-size:12pt">all
the opportunities for all the manipulative strategies
that are offered by all the methods other than MJ
</span><span style="line-height:107%;font-size:12pt">(Belinski & Laraki, Majority Judgment,
pp.14, 15, 189-198, 212, 245, 282-292)</span><span style="line-height:107%;font-size:12pt">. (I assume
that your mathematical knowledge is currently much
superior to mine.<span>
</span>Consequently, I’m hoping that you will be able to
tell me whether the above B&L claim of ‘almost half’
is fully justified by B&L’s mathematical proofs.)</span></p>
<p style="color:rgb(0,0,0);font-family:calibri,sans-serif;font-size:11pt;font-style:normal;font-weight:normal;margin-top:12pt;margin-bottom:0pt">
<span style="line-height:107%;font-size:12pt">If it is
fully justified, MJ would have this advantage over IRV
and MAM.<span>
</span>I say this even though it still seems to me that,
in any case, it would also be extremely unlikely that
strategic voting would be successful when using IRV or
MAM to elect one winner by millions of voters.</span></p>
</li>
<li style="color:rgb(0,0,0);font-family:calibri,sans-serif;font-size:12pt;font-style:normal;font-weight:normal">
<p style="color:rgb(0,0,0);font-family:calibri,sans-serif;font-size:11pt;font-style:normal;font-weight:normal;margin-top:12pt;margin-bottom:0pt">
<span style="line-height:107%;font-size:12pt">I still
favor MJ even though it is theoretically vulnerable to
‘Later-no-harm’ (LNH).<span>
</span>I am currently persuaded by B&L that this
could occur in practice only in an election composed of
voters and candidates whose numbers could be counted on
one person’s hands.
<span> </span></span><span style="line-height:107%;font-size:12pt">This is confirmed by Jameson in his 1st
informative and recent EM posts: 1): ‘there is the
failure of the later-no-harm (LNH) criterion. But note:
MJ actually does pass a weaker version of LNH: rating
additional candidates at above bottom will not harm the
winner as long as those candidates are ranked below the
winning median. My claim is that over time, the winning
median grade will mostly fall in a given band of grades;
for instance, using letter grades, between B- and D+. In
that case, making distinctions between A and B at the
top or D and F at the bottom are strategically safe.’ </span></p>
</li>
<li style="color:rgb(0,0,0);font-family:calibri,sans-serif;font-size:12pt;font-style:normal;font-weight:normal">
<p style="color:rgb(0,0,0);font-family:calibri,sans-serif;font-size:11pt;font-style:normal;font-weight:normal;margin-top:12pt;margin-bottom:8pt">
<span style="line-height:107%;font-size:12pt">Similarly,
I am aware that MJ fails the strong Independence of
Irrelevant Alternative (IIA) candidates test.
<span> </span>However,</span><span style="line-height:107%;font-size:12pt"> B&L explain how MJ does at least pass a
weaker IIA test</span><span style="line-height:107%;font-size:12pt">.<span>
</span>As Jameson put in his 2<sup>nd</sup> recent and
informative EM contribution:
</span><span style="line-height:107%;font-size:12pt">‘Note that this strategy will almost certainly
not affect the medians, and thus will not change the
winner. Though technically it breaks IIA, it only does
so in bizarre cases where both voter and candidate
distributions differ severely from historical norms.’</span></p>
</li>
</ol>
<p style="margin:12pt 0in 8pt"><span style="line-height:107%;font-size:12pt"><font face="Calibri">S: I would very much
appreciate anyone explaining why you think any of the
above views are mistaken.<span>
</span>Please try to correct any mistakes you have noticed
in the above.</font></span></p>
<p style="margin:0in 0in 8pt"><span style="line-height:107%;font-size:12pt"><font face="Calibri">I look forward to
hearing from you,</font></span></p>
<p style="margin:0in 0in 8pt"><span style="line-height:107%;font-size:12pt"><font face="Calibri">Steve</font></span></p>
<br>
</div>
<br>
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