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<b><span style="color: black; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">From:</font></span></b><font face="Calibri"><span style="color: black; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;">
Kristofer Munsterhjelm <km_elmet@t-online.de><br>
<b>Sent:</b> Tuesday, February 14, 2017 9:41 PM<br>
<b>To:</b> steve bosworth; election-methods@lists.electorama.com; <br>
<b>Subject:</b> Re: [EM] “goal of a better election method”</span><span style="color: black; font-size: 14pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;">
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<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">Hi Kristofer,</font></span></p>
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<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">S: Thank you for your helpful suggestions and carefully
detailed analysis of my suggestions.<br>
Again, I look forward to your feedback.<br>
<br>
K: I suppose the concern that comes most clearly to mind is that MJ is not<br>
meant to be a cardinal method, whereas using averages introduces a<br>
cardinal (numeric) element.<br>
<br>
To rephrase that, all that "plain" MJ knows about is that there's a<br>
common standard among the people where<br>
<br>
Excellent is better than Very Good<br>
Very Good is better than Good<br>
Good is better than Acceptable<br>
Acceptable is better than Poor<br>
and Poor is better than Reject.<br>
<br>
It doesn't know what the common standard *is*, however.</font></span></p>
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<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">S:<span style="mso-spacerun: yes;">
</span>But of course MJ counts each “grade” given to each candidate by a voter at least as if it was given “honestly” according to each voter’s judgment of the extent to which each candidate comes close to that voter’s idea of an “excellent” candidate for the
office.<span style="mso-spacerun: yes;"> </span>In this limited B&L sense, each of these “ideas” is “absolute” rather than “relative”, i.e. capable of be defined using a common language.<br>
<br>
K:<span style="mso-spacerun: yes;"> </span>To use a school grading metaphor, it knows that A is better than B, but<br>
not that<br>
A: 100%-97% of max attainable points<br>
B: 97%-85%<br>
(or what have you).</font></span></p>
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<font face="Calibri"><span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;">S:
<span style="mso-spacerun: yes;"> </span>As I understand it, you are largely correct and it accords with B&L’s presentation.<span style="mso-spacerun: yes;">
</span>They clearly say that MJ’s “language measures are …. not cardinal ….” (p.168), but, at the same time, “nor are they merely ordinal” (p.168).<span style="mso-spacerun: yes;">
</span>Accordingly, B&L correctly go on to describe how “grades” can become clearly defined by “learning and practice”, e.g. and “experience professor … has a well-developed set of benchmarks that together define absolute evaluations that dominate the relative
comparisons” (p.168) of student performance.<span style="mso-spacerun: yes;"> </span>
In my own experience as a university professor, each teacher was required to publish the different sets of “learning outcomes” that a student would have to display in order to receive any one of the following “grades”:<span style="mso-spacerun: yes;">
</span>A, B, C, D, or F. <span style="mso-spacerun: yes;"> </span>B&L add that the “same is true of voters: they have seen and learned about able statesmen, presidents and prime ministers …, as well as inept or corrupt officeholders.<span style="mso-spacerun: yes;">
</span>They also have clear benchmarks.” <span style="mso-spacerun: yes;"> </span>Perhaps B&L would also say that even when some numbers are used as alternative expressions of such linguistically defined grades, this can be an examples of what they say at the
top of page 48 of your first refere</span><span style="font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;">nce below:</span></font></p>
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<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-family: "Times-Roman",serif; font-size: 10pt; mso-bidi-font-family: Times-Roman;">“ ... there may well be situations where the numbers are at once a common</span></p>
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<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-family: "Times-Roman",serif; font-size: 10pt; mso-bidi-font-family: Times-Roman;">language and an interval measure: possible examples are those used in evaluating</span></p>
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<span style="font-family: "Times-Roman",serif; font-size: 10pt; mso-bidi-font-family: Times-Roman;">wines, divers, and figure skaters, where the judges are professionals who have</span></p>
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<span style="font-family: "Times-Roman",serif; font-size: 10pt; mso-bidi-font-family: Times-Roman;">learned the meanings of the numbers and scales.”</span></p>
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<span style="font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">Still, I accept that HMJ dep<span style="color: black;">arts from
B&L’s clear statement that “grades” are “not cardinal because adding them makes no sense” (p.168).<span style="mso-spacerun: yes;">
</span>Nevertheless, might it not be argued that HMJ appropriately honors the middle position that its “grades” have as a result of them not being “merely ordinal” as explained above, i.e. HMJ only averages the “grades” to the left of each “median-grade” and
including this median-grade.<span style="mso-spacerun: yes;"> </span>In this way, might not HMJ still be able to claim that HMJ is less subject to anti-democratic “manipulation” than all the other single-winner methods that sum or average all the citizen’s
votes, i.e. not less by MJ’s “about half” but still less?<span style="mso-spacerun: yes;">
</span></span></font></span></p>
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<p style="background: white; margin: 0in 0in 11.25pt; line-height: normal; vertical-align: bottom;">
<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">K:<span style="mso-spacerun: yes;">
</span>Suppose that we want to use MJ to determine the student with the best<br>
performance. Then MJ is supposed to work equally well no matter whether<br>
the grading scale is<br>
<br>
A: 100%-97%<br>
B: 97%-80%<br>
(... etc)<br>
<br>
of if the grading scale is<br>
<br>
A: 100%-92%<br>
B: 92%-77%<br>
(... etc)<br>
<br>
as long as all classes use the same grading scale (that's the "common<br>
standard" qualification).</font></span></p>
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<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">If you use averaging as part of an MJ method, then the
ordinal<br>
assumption is violated, because taking the mean doesn't just depend on<br>
the relative order (i.e. A is better than B), but also on just how much<br>
(A has a mean score of 98.5%, B has a mean score of 88.5% vs A has a<br>
mean score of 96% and B has a mean score of 84.5%).<br>
<br>
S:<span style="mso-spacerun: yes;"> </span>Given the above, like B&L I see HMJ’s and MJ’s “grades” as not determined by numbers or percentages but by different sets of “learning outcomes”, qualities, or “benchmarks” that can be defined by a “common language”.<br style="mso-special-character: line-break;">
<br style="mso-special-character: line-break;">
</font></span></p>
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<p style="background: white; margin: 0in 0in 11.25pt; line-height: normal; vertical-align: bottom;">
<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">K: As a consequence, the method may produce better results
in certain<br>
scenarios (where the common standard is equally spaced), but it trades<br>
that off by potentially producing worse results in other scenarios<br>
(where the common standard is not equally spaced).</font></span></p>
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<p style="background: white; margin: 0in 0in 11.25pt; line-height: normal; vertical-align: bottom;">
<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">Or more simply put: making the scale cardinal, which
you need to be able<br>
to calculate means on the votes, adds more assumptions that may not be true.<br>
For more on this particular objection, see B&L's "Election by Majority<br>
Judgment: Experimental Evidence", p 45. and onwards ("Voting by Points<br>
and Summing"). Quoting:<br>
<br>
>> But, is it reasonable to use numerical scales in voting? The answer is a resounding<br>
>> no, for several reasons.</font></span></p>
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<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">S:<span style="mso-spacerun: yes;">
</span>But I see that B&L continue with this quote as follows: “</font></span><span style="font-family: "Times-Roman",serif; font-size: 10pt; mso-bidi-font-family: Times-Roman;">But, is it reasonable to use numerical scales in voting? The answer is a resounding
no, for several reasons.<span style="mso-spacerun: yes;"> </span>First, the numbers mean nothing unless they are defined: proposals to use weights give them no definition. Their only real “meaning” is found in their strategic use.<span style="mso-spacerun: yes;">
</span>This induces comparisons, which immediately leads to Arrow’s paradox.”</span><span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><br style="mso-special-character: line-break;">
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</font></span></p>
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<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">Firstly, given the above earlier discussion, each of
HMJ’s “numbers” would be used only when breaking ties, and each would be “defined”.</font></span></p>
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<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">Secondly, these numbers would not be on the HMJ ballots
used by voters.<span style="mso-spacerun: yes;"> </span>Such ballots would seem much less likely to “induce comparisons … leading to Arrow’s pardox”.<br style="mso-special-character: line-break;">
<br style="mso-special-character: line-break;">
</font></span></p>
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<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">K: (My source is<br>
</font></span><a id="LPlnk296764" href="https://1984f707-a-62cb3a1a-s-sites.googlegroups.com/site/ridalaraki/xfiles/ElectionByMajorityJudgment(ExperimentalEvidence)Final.pdf" previewremoved="true"><span style="color: blue; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">https://1984f707-a-62cb3a1a-s-sites.googlegroups.com/site/ridalaraki/xfiles/ElectionByMajorityJudgment(ExperimentalEvidence)Final.pdf</font></span></a><span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">)<br>
<br>
>From an MJ point of view, only using an inferred numerical scale for<br>
tiebreaking is surely better than using it everywhere (like in Range).<br>
But the same theoretical arguments apply as soon as you're using a<br>
numerical scale at all.<br style="mso-special-character: line-break;">
<br style="mso-special-character: line-break;">
</font></span></p>
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<p style="background: white; margin: 0in 0in 11.25pt; line-height: normal; vertical-align: bottom;">
<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">S: Given the above and while the “spaces” between HMJ’s
and MJ’s<span style="mso-spacerun: yes;"> </span>6 “grades” cannot claim to be exactly equal, perhaps we can still say that B&L’s electoral experiments and tests in France and elsewhere using MJ, give us a reason to say the following:<span style="mso-spacerun: yes;">
</span>In contrast to B&L’s own “majority-guage” and “majority-value” procedures for breaking ties, HMJ’s limited averaging would probably provide us with some additional useful information for breaking ties, i.e. HMJ’s “approximate” averages are likely to
reveal a slightly sharper view of the different intensities with which the majority of voters value each candidate as “fit” for the office.?<span style="mso-spacerun: yes;">
</span>What do you think?<br>
<br>
K: There's also a strategy argument, which could be generally argued like this:<br>
<br>
- Either ties of the type where many candidates have the same median are<br>
common or they're not.<br>
- If they're not common, then a mean tiebreak is not going to change the<br>
outcome often, so we can go with Bucklin or MJ's system.<br style="mso-special-character: line-break;">
<br style="mso-special-character: line-break;">
</font></span></p>
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<p style="background: white; margin: 0in 0in 11.25pt; line-height: normal; vertical-align: bottom;">
<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">S:<span style="mso-spacerun: yes;">
</span>However, if my above suggestion is valid, HMJ’s mean score of each candidates’ grades to the left of her ‘median-grade” and including her median-grade would be better, even if it only makes a difference rarely.</font></span></p>
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<p style="background: white; margin: 0in 0in 11.25pt; line-height: normal; vertical-align: bottom;">
<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">K:<span style="mso-spacerun: yes;">
</span>- If they're common, then, since Range is more susceptible to strategy<br>
than MJ, using a mean tiebreak will make HMJ considerably more<br>
susceptible to strategy as well, and so should be avoided.</font></span></p>
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<p style="background: white; margin: 0in 0in 11.25pt; line-height: normal; vertical-align: bottom;">
<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">S:<span style="mso-spacerun: yes;">
</span>While HMJ might be slightly more “susceptible to strategy” than MJ, am I correct in thinking it would not be as susceptible as Range?</font></span></p>
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K: See this slide set by B&L for more on that:<br>
</font></span><a id="LPlnk888770" href="http://igm.univ-mlv.fr/AlgoB/algoperm2012/01Laraki.pdf" previewremoved="true"><span style="color: blue; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">http://igm.univ-mlv.fr/AlgoB/algoperm2012/01Laraki.pdf</font></span></a><span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">
. In particular</font></span></p>
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<p style="margin: 15pt 0in 0pt; line-height: 15pt;"><span style="color: rgb(102, 102, 102); font-family: wf_segoe-ui_normal; font-size: 10.5pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman";">Traditional Methods and results
Incompatibility Between Electing and Ranking Majority Judgement: Two Applications Majority Judgement Measuring, Ranking and Electing</span></p>
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they say:<br>
<br>
"The unique [social grading function]s that are partially<br>
strategy-proof-in-ranking are the order functions."<br>
<br>
This means that the only grade-based voting methods that are partially<br>
strategy-proof in ranking (which they define earlier) are order<br>
functions, which are of the form "return the nth best grade" for some n.<br>
(The median sets n=voters/2) Consequentially, to keep the SGF partially<br>
strategy-proof-in-ranking, the tiebreak should also be an order function<br>
with a different n, which it is in MJ and Bucklin, but not in HMJ.<br>
<br>
B&L do not analyze the HMJ variant in itself, but they note:<br>
<br>
"The unique aggregation functions that minimize the probability of<br>
effective-manipulability are the middlemost. Point-summing-methods, f_1<br>
and f_n maximize this probability."<br>
<br>
which does suggest that using a point-summing method as a tiebreak will<br>
weaken the method more than using another type of method.</font></span></p>
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<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri"> </font></span></p>
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<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">S: Yes, partially weaken HMJ with regard to manipulation
resistance, but perhaps also giving HMJ the advantage of discovering more exactly the candidate who is most highly valued as “fit” for the office.<span style="mso-spacerun: yes;">
</span>Also, HMJ seems to use a tie breaking procedure which would be easier for ordinary voters to understand.<span style="mso-spacerun: yes;">
</span>Consequently, perhaps HMJ would still reduce its vulnerability to “manipulation” by about 20% rather than MJ’s ”about half”.<span style="mso-spacerun: yes;">
</span>Is this something one could calculate more exactly by using something like B&L’s formula on pages 197-8 (Majority Judgment, 2011, MIT) or the slide 171 on the second source you referred me to ?<span style="mso-spacerun: yes;">
</span>I hope you can sharpen my understanding of these calculations.<br>
<br>
K: In addition, averaging would make a method no longer<br>
strategy-proof-in-grading. For the same reason that the median (being an<br>
order function) makes MJ resistant to strategy, an order function tie<br>
break makes MJ resistant to strategy in the tiebreak. B&L say:<br>
<br>
"The unique strategy-proof-in-grading SGFs are the order functions.<br>
<br>
If the mechanism is a point-summing method (the mean with respect to<br>
some parametrization), for almost all profiles, all voters can manipulate."</font></span></p>
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<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri"> </font></span></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"><span style="color: black; line-height: 107%; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;">S:<span style="mso-spacerun: yes;">
</span>If so, such <span style="mso-spacerun: yes;"> </span>a potential for “manipulation” would seem to be more reduced if my currently proposed HMJ (i.e. HMJ(1)) were modified to become HMJ(2) as follows: The tie breaking procedure to be changed so that only
the candidates who had received the “highest median-grade” would be considered as potential winners, i.e. only the “grades” received by these candidates to the left of their common “highest median-grade” and including this “highest median-grade” would be used
to calculate their different mean scores of evaluation.<span style="mso-spacerun: yes;">
</span>In this way, HMJ(2) would seem to retain the feature you mention in the last sentence of your additional thoughts below:<span style="mso-spacerun: yes;">
</span>“</span><span style="color: black; line-height: 107%; font-size: 10pt; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;">only an order function will do for the main scoring prior to any tiebreaker”.<span style="mso-spacerun: yes;">
</span></span><span style="color: black; line-height: 107%; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;">Perhaps this modification would reduce HMJ(2)’s
vulnerability to “manipulation” by about 30% rather than <span style="mso-spacerun: yes;">
</span>either HMJ’s(1)’s by about 20% or <span style="mso-spacerun: yes;"> </span>MJ’s by “about half”.
<span style="mso-spacerun: yes;"> </span></span><span style="color: black; line-height: 107%; font-size: 10pt; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><span style="mso-spacerun: yes;"> </span></span></font><span style="color: black; line-height: 107%; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">What
do you think?<br>
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K: (Last slide on "Strategy in Grading")<br>
<br>
This is not to say that HMJ is a *bad* method. I would certainly choose<br>
it if the alternative was, say, IRV or Borda. But using averaging does<br>
undermine B&L's theoretical foundation of MJ (since it is no longer an<br>
ordinal grade method), and if you accept their strategy-resistance<br>
arguments, it also weakens MJ's resistance to strategy.</font></span></p>
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<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri"> </font></span></p>
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<span style="color: black; font-size: 10pt; mso-ascii-font-family: Calibri; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri">S:<span style="mso-spacerun: yes;">
</span>Given now that we have 2 different formulations of HMJ to consider, as well as MJ and a number of other somewhat attractive single-winner methods, I would very much appreciate receiving your reasons for currently most favoring one of them for electing
a president.</font></span></p>
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<p style="margin: 0in 0in 8pt;"><span style="color: black; line-height: 107%; font-size: 10pt; mso-ascii-font-family: Calibri; mso-hansi-font-family: Calibri; mso-bidi-font-family: Calibri;"><font face="Calibri"><span style="mso-spacerun: yes;"> </span>[...]<br>
<br>
K:<span style="mso-spacerun: yes;"> </span>I forgot to mention this strategy-in-grading problem.<br>
<br>
Suppose we're using ordinary MJ, and candidate X's final grade is Good.<br>
Someone who gave X a grade of "Very Good" has no reason to exaggerate to<br>
"Excellent" because his vote is counted equally according to MJ's tie<br>
breaker. This helps prevent the method from becoming Really Expensive<br>
Approval where everybody just votes max or min.<br>
<br>
However, if you use averages as a tiebreak, the voter might think: "I'm<br>
reasonably sure X's final grade is going to be Good, but as there may be<br>
other candidates with Good as a final grade as well, I should do my best<br>
to make sure X's average gets as high as possible, which means that I<br>
should vote Excellent instead of Very Good". If enough voters do that,<br>
then the method slides into Approval.<br>
<br>
And since we need all the help we can get to keep MJ from becoming<br>
Approval (some Range advocates say that MJ would essentially become<br>
Approval even in its current state), it's best to make this kind of<br>
strategy ineffective. And B&L say that requirement narrows down the only<br>
tiebreakers you can use into order functions -- for the same reason that<br>
only an order function will do for the main scoring prior to any tiebreaker.</font></span></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">S:<span style="mso-spacerun: yes;">
</span>Thank you, I look forward to your feedback.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Steve</font></p>
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