آیا انتخابات منصفانه است؟


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آیا انتخابات منصفانه است؟
by Ari Siletz
02-Mar-2012
 

نخیر، منظور این نیست که انتخابات جمعه در ایران درست اجرا شد یا نه‌. اگر جوابش به این آسونی‌ها بود که ارزش بلاگ کردن نداشت. مساله بنیادی تر از این هاست. بعضی‌ انتخابات جوری هستند که اگر حضرت سلیمان هم مسئولش بود (این حضرت در اجرای عدالت خیلی‌ وضعش خوب بود) و همه آرا به درستی‌ شمرده میشد، باز هم سر مردم کلاه میرفت. به عنوان مثل مسابقه‌ای سه طرفه بین آقا موشه، خاله سوسکه، و لؤلؤ خور خوره را در نظر بگیرید.

۲۰۰ نفر رای دهنده (فرض کنیم همه شون قزوینی هستند) این ۳ شخصیت را به ترتیب ترجیح اینطور ارزیابی میکنند:

۱. موش ۲. لؤلؤ، ۳. سوسک

۱۹۵ رای دهنده رشتی داریم که ترجیح آنها به این ترتیب است:

۱.`سوسک ۲. لؤلؤ ۳.موش

۲۰ تا رای دهنده در بقیه موندن (تبریزی ها) که ترتیب ترجیح آنان اینطور است:

۱. لؤلؤ ۲.سوسک ۳. موش

خوب با این وضع آقا موشه نماینده مجلس میشه چون ۲۰۰ نفر قزوینی بهش رای دادن. خاله سوسکه دوم میشه چون ۱۹۵ نفر رشتی به او رای دادند. بدبخت لؤلؤ با فقط ۲۰ رای تبریزی‌ها سوم میشه. ولی‌ اینطور رای شماری رایج و بنظر منطقی‌ انتخاب مردم را به ترتیب ترجیح به درستی‌ نمیرساند. حالا چرا، توضیحش این است که اگر نامزد هارا دو تا دو تا مقایسه کنیم و اونطوری بشمریم لؤلؤ برنده میشه:

اینطوری حساب کنید: ۱۹۵ رشتی لؤلؤ را به آقا موشه ترجیح میدهند. ۲۰ نفر تبریزی هم باز لؤلؤ را به آقا موشه ترجیح میدهند. در جمع شد ۲۱۵ نفر (رشت + تبریز) که لؤلؤ را به آقا موشه ترجیح میدهند. از آن طرف فقط اون ۲۰۰ قزوینی آقا موشه رو به لؤلؤ ترجیح میدن. پس در این انتخابات که ۲۱۵ نفر لؤلؤ رو به آقا موشه ترجیح میدان و فقط ۲۰۰ نفر آقا موشه رو از لؤلؤ بیشتر دوست دارن چرا آقا موشه برنده شد؟

خلاصه میگم مواظب باشین قزوینی‌ها سرتون کلاه نذارن، کلک بازی شون خوبه.

برای بهبود وضع به این مقاله مراجعه کنید.


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Ari Siletz

Couple of replies

by Ari Siletz on

Aynak: Glad you enjoyed the blog. The U.S. elections system certainly has the flaws you mentioned, and of course those flaws have arguments both for and against. For example the two senator per state rule (with congressional representation in proportion to popluation) makes sure more populated states don't overwhelm the interests of the less populated states. This issue was argued at length in the Connecticut Compromise of 1787.

Maghshoosh: Thanks for digging up the Dasgupt-Maskin paper. The authors do quickly point out that the "dictator conclusion" while satisfying the consensus, transitivity, irrelevant candiate principles, does not satisfy the important anonymity/neutrality principle where no voter is more important than another. But it is fascinating that in a strictly logical sense (where, for example, auxilliary ideological factors are not there to guarantee transitiviy) the only way to satisfy the first three conditions is to have a dicatorship! Also, I wonder (wished) if in finding the most effective way to sabotage the Iran Majles elections, the opposition leaders consulted experts familiar with voting theory.

 


maghshoosh

How about more elaborate decision-making algorithms?

by maghshoosh on

Although the referenced SciAm article is for sale, one of the authors has posted it under a different title at his website for download.  I wasn't familiar with this topic and have only skimmed through the (SciAm) article, but it doesn't look like the authors have covered more elaborate possibilities.  E.g., in considering either the 3-candidate scenario portrayed in the blog or the rank-order voting discussed in the article, why should the ordering among the candidates be done in a uniform manner? 

For instance, in the blog example, moosh-more-votes-than-looloo is treated the same as looloo-more-votes-than-soosk.  But maybe they should be weighted based on the number of votes each candidate got or some vote differential among the candidates.  Similarly, in the article, the authors assign uniformly-separated points in the rank-ordering method, so that with for example 4 candidates, a voter gives 4 points to his favorite pick, 3 to next favorite and so on.  But maybe voters should be allowed non-uniform spacing in assigning points to their candidates.

I don't know how more elaborate considerations such as these would affect the results, like the Arrow Impossibility Theorem, mentioned in the article.  I presume someone's looked at these kind of algorithms.  One problem with such elaborations is that if the methodology looks too complicated to the electorate, they may not approve of it.  People prefer simpler methods that are easy to follow.

But the article is disingenous in one glaring respect.  It states on p.12 that, "any electoral method that satisfies the principles of consensus, independence of irrelevant alternatives, and transitivity must be a dictatorship; that is, the method must have the property that only a single voter (the dictator) matters."  That single happy voter is none other than the Supreme Leader.  In other words, back in 2003 the authors had, through the irrevocable force of logic & reason, arrived at the conclusion that the IRI's is the most ideal voting system.  But do you see them admitting to it?


aynak

That's partly how Al Gore "lost" to W' the war criminal

by aynak on


That mixed with of course out right cheating, in 2000 election.

Electerol college is a flawed system that ineeded can leave the outcome of an election instead of  to a simple --popular-- vote to some loophole which by definition will/can be used by  the party that is going to fall short in total number of votes.  Of course this is in boundry case and very rare, but still possible as the world witnessed and your example shows.

U.S democracy can be improved in 3 areas:

1-Removal of winner takes all in the 2 party system and replacing it by proportional representation.

2-Each states --regardless of population-- having 2 senators

3-Electoral college for U.S president

Ari is correctly pointing out at how the 3'rd one can lead to the issue of a less popular president winning the who less, but the first issue is even more interesting:

The winner all does not actually help mutli party system, as we have seen from U.S inception, (Federalists/Anti-federalist all the way to now:  Republican/Democrat), in fact looking back at how it all started in U.S with a single party in U.S it can be questioned if the founding fathers even see good in it.

But the reality is, if a group has  5% of the vote that group represents 5% of people and has to have 5% voice.   THat would lead to coalition building.   

To be fair, porportional represenation can also lead to small group actually coming to dictate the outcome *again* on a boundry condition situation.   But in general, and setting boundry/corner cases aside, it is more represnatative *because* it allows for more voices to be heard.

 

Thanks for a good blog Ari.

 


پندارنیک

........

by پندارنیک on

Elections don't have to be fair and just..............they are held to be effective........


Ari Siletz

Siamak

by Ari Siletz on

The blog says that in a three way race (or more), the candidate with the most votes isn't necessarily the preferred candidate by the voters! It gives a simple example of this paradox (you'll see it once you follow the blog example numbers and voter preference order carefully in the blog). The linked Scientific American artilce abstract (full article needs to be purchased) goes into the mathematics of the logical error in the "majority" vote concept and ways to fix the problem.  This unintiuitve and interesting  result is unelated to the politics of the democratic process.It just says that in a three way race where the  higest vote count wins, the people may end up electing the least preferred candidate.


Siamak Asadian

Only because

by Siamak Asadian on

National elections in the US, or France (or for that matter most countries in the world!) are a sham, it still doesn't mean elections (as a civilized means of gauging public mandate) are irrelevant or unimportant. Bourgeoisie by definition is wary of a true, substantial participatory democracy. Then again Proletarian tradition hasn't been all that great either. Some might even argue, have argued, it's actually been a lot worse.

Make a long story short: please don't underestimate the significance and importance of voting as a process, institution, and a tradition in establishing, augmenting and preservation of people's rule.

Hopeful recent cases that restored my faith in the process of popular voting: recalls in US states of Ohio, and Wisconsin currently underway. Cheers