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<div dir="ltr" data-setdir="false">Hi Kristofer,</div><div><br></div>
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Le mercredi 29 juillet 2020 à 12:45:02 UTC−5, Kristofer Munsterhjelm <km_elmet@t-online.de> a écrit :
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<div style="font-size: 13px;">On 16/07/2020 02.02, Kevin Venzke wrote:<br></div><div style=""><div dir="ltr" style="font-size: 13px;">>>> I was thinking about the possibility of using the mechanism to direct a<br clear="none">>>> government or organization to act in a minmax manner: one that intend to<br clear="none">>>> make the worst off best off, rather than improve the condition of the<br clear="none">>>> median voter.<br clear="none">>> <br clear="none">>> Just to interject quickly. To my mind these two things are (naively)<br clear="none">>> the same, and if results matched the preference of the median voter<br clear="none">>> you would have a good thing. What I expect instead, with two factions<br clear="none">>> fighting over who can capture a majority, is that the factions don't<br clear="none">>> propose (or don't enact) the median position. They want the vote of<br clear="none">>> that position, and those voters can come to the victory party, but<br clear="none">>> they won't be in control.<br clear="none">><br clear="none">>Doesn't the pizza election show that these are not the same? Suppose the<br clear="none">>utilities are:<br clear="none">><br clear="none">>7 voters: Pepperoni 9, Mushroom 8<br clear="none">>3 voters: Pepperoni 0, Mushroom 9</div><div dir="ltr" style="font-size: 13px;"><br></div><div dir="ltr" data-setdir="false" style=""><font size="3">Absolutely it shows that they aren't exactly the same. I understand what you are saying,</font></div><div dir="ltr" data-setdir="false" style=""><font size="3">so it becomes maybe a terminology issue that may not be of interest. But for me there are</font></div><div dir="ltr" data-setdir="false" style=""><font size="3">three concepts here:</font></div><div dir="ltr" data-setdir="false" style=""><font size="3">1. the minmax objective, as you say.<br></font></div><div dir="ltr" data-setdir="false" style=""><font size="3">2. enacting the median voter's position, which is how I would interpret "improve the condition</font></div><div dir="ltr" data-setdir="false" style=""><font size="3">of the median voter," though I understand this is not really the concept you </font><span style="font-size: medium;">are using in</span></div><div dir="ltr" data-setdir="false" style=""><span style="font-size: medium;">the pizza example.</span></div><div dir="ltr" data-setdir="false" style=""><font size="3">3. the result you might expect from a majoritarian or strategic Range election, meaning</font></div><div dir="ltr" data-setdir="false" style=""><font size="3">merely that the median voter will be included in the victorious majority.</font></div><div dir="ltr" data-setdir="false" style=""><font size="3"><br></font></div><div dir="ltr" data-setdir="false" style=""><font size="3">You can see the potential for difference between 2 and 3 by putting "heavy pepperoni" </font></div><div dir="ltr" data-setdir="false" style=""><font size="3">and "light pepperoni" in your example and arranging it on a spectrum, placing a small</font></div><div dir="ltr" data-setdir="false" style=""><font size="3">number of "light pepperoni" supporters at the median. It becomes unclear whether "light"</font></div><div dir="ltr" data-setdir="false" style=""><font size="3">will win under a majoritarian method. It's only clear that some pepperoni option will win.</font></div><div dir="ltr" data-setdir="false" style=""><font size="3"><br></font></div><div dir="ltr" data-setdir="false" style=""><font size="3">What I mean by 1 and 2 being "naively the same" is that if you generate scenarios </font></div><div dir="ltr" data-setdir="false" style=""><font size="3">randomly in issue space, they are probably the same. Or at least similar enough that</font></div><div dir="ltr" data-setdir="false" style=""><font size="3">if it's easier to address the problem by focusing on 2 and not 1, maybe that's worth it.</font></div><div dir="ltr" data-setdir="false" style=""><font size="3"><br></font></div><div dir="ltr" data-setdir="false" style=""><font size="3">The pizza scenario highlights the situation where 1 differs from 2 and 3. But I think it's</font></div><div dir="ltr" data-setdir="false" style=""><font size="3">more common that 3 is the outlier. That disturbs me because it seems that 2 should be</font></div><div dir="ltr" data-setdir="false" style=""><font size="3">achievable without even deviating from majoritarian principles.</font></div><div dir="ltr" data-setdir="false" style=""><br></div><div dir="ltr" style=""><div class="ydpf046eb46yqt1370504810" id="ydpf046eb46yqtfd50372" style=""><font size="3"><br clear="none"></font><span style="font-size: 13px;">>> When you say "to make the consensus option at least as good" do you</span><br clear="none"><span style="font-size: 13px;">>> envision some kind of mechanism that could actually improve what the</span><br clear="none"><span style="font-size: 13px;">>> consensus option is? Or maybe, easier to imagine: a rule that imposes </span><br clear="none"><span style="font-size: 13px;">>> some kind of universal penalty if consensus isn't achieved. A forfeiture of </span><br clear="none"><span style="font-size: 13px;">>> office seems like the most obvious.</span></div><span style="font-size: 13px;">></span><br clear="none"><span style="font-size: 13px;">></span><br clear="none"><span style="font-size: 13px;">>I was thinking that the random ballot outcome can be quite bad. E.g. the</span><br clear="none"><span style="font-size: 13px;">>expected scores in the two-sided pizza election:</span><br clear="none"><span style="font-size: 13px;">></span><br clear="none"><span style="font-size: 13px;">>6 pepperoni voters: 7.0</span><br clear="none"><span style="font-size: 13px;">>2 anchovy voters: 3.4</span><br clear="none"><span style="font-size: 13px;">>2 mushroom voters: 1.8</span><br clear="none"><span style="font-size: 13px;">></span><br clear="none"><span style="font-size: 13px;">>If someone blinks (e.g. an anchovy voter mistakenly doesn't set mushroom</span><br clear="none"><span style="font-size: 13px;">>as the consensus option), then the outcome is not particularly good for</span><br clear="none"><span style="font-size: 13px;">>society as a whole. All we *really* need is the expectation of the</span><br clear="none"><span style="font-size: 13px;">>lottery to be less than the consensus option, while resisting strategy.</span><br clear="none"><span style="font-size: 13px;">>So in some ideal world, the expected value for the fair lottery would be</span><br clear="none"><span style="font-size: 13px;">>something along the lines of</span><br clear="none"><span style="font-size: 13px;">></span><br clear="none"><span style="font-size: 13px;">>6 pepperoni voters: 8 - epsilon</span><br clear="none"><span style="font-size: 13px;">>2 anchovy voters: 8 - epsilon</span><br clear="none"><span style="font-size: 13px;">>2 mushroom voters: 9 - epsilon</span><br clear="none"><span style="font-size: 13px;">></span><br clear="none"><span style="font-size: 13px;">>and even for very small epsilon, it would still be preferable to choose</span><br clear="none"><span style="font-size: 13px;">>the mushroom consensus option. But how to implement such a lottery, much</span><br clear="none"><span style="font-size: 13px;">>less in a strategy-resistant manner, I have no idea.</span><br clear="none"><span style="font-size: 13px;">></span><br clear="none"><span style="font-size: 13px;">>In a way, it's like the concept of MAD: if you give every voter his</span><br clear="none"><span style="font-size: 13px;">>personal doomsday button to push if he doesn't get a satisfactory</span><br clear="none"><span style="font-size: 13px;">>outcome, then minmax will happen if it's at all achievable. However, the</span><br clear="none"><span style="font-size: 13px;">>outcome should consensus be impossible is truly horrible. The better the</span><br clear="none"><span style="font-size: 13px;">>system can be in the "no consensus" case while leaving consensus</span><br clear="none"><span style="font-size: 13px;">>preferable, the better the method is.</span><br clear="none"><span style="font-size: 13px;">></span><br clear="none"><span style="font-size: 13px;">>The other side of that coin is what I said in the earlier post: if the</span><br clear="none"><span style="font-size: 13px;">>consensus option is always at least as good as a random ballot, then</span><br clear="none"><span style="font-size: 13px;">>it'll always be chosen. So making the structure around the mechanism</span><br clear="none"><span style="font-size: 13px;">>conducive to finding a consensus would also help.</span><br clear="none"><span style="font-size: 13px;">></span><br clear="none"><span style="font-size: 13px;">>We'd have to be careful that the alternative to consensus isn't biased,</span><br clear="none"><span style="font-size: 13px;">>though. "Forfeiting one's office" might well be, just like "status quo</span><br clear="none"><span style="font-size: 13px;">>prevails" is.</span><div class="ydpf046eb46yqt1370504810" id="ydpf046eb46yqtfd08550" style="font-size: 13px;"><br clear="none"></div><div class="ydpf046eb46yqt1370504810" id="ydpf046eb46yqtfd08550" dir="ltr" data-setdir="false" style=""><font size="3">Yes, you're right. There would at least need to be a clear cost to the </font></div><div class="ydpf046eb46yqt1370504810" id="ydpf046eb46yqtfd08550" dir="ltr" data-setdir="false" style=""><font size="3">participants for forfeiture of office to be an effective tool.</font></div><div class="ydpf046eb46yqt1370504810" id="ydpf046eb46yqtfd08550" dir="ltr" data-setdir="false" style=""><font size="3"><br></font></div><div class="ydpf046eb46yqt1370504810" id="ydpf046eb46yqtfd08550" dir="ltr" data-setdir="false" style=""><font size="3">Kevin</font></div><div class="ydpf046eb46yqt1370504810" id="ydpf046eb46yqtfd08550" dir="ltr" data-setdir="false" style="font-size: 13px;"><br></div></div></div>
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