The Condorcet Paradox and Arrow's Impossibility Theorem

[Aviator]

Democracy is Either Impossible or Arbitrary

In the modern Western world, the idea that democracy is the greatest form of government has nearly become fact. The basis of this belief is that democracy is able to reflect the will of the people through elections. However, further study of the way a democracy works proves that no such thing occurs, and that an elected leader does not reflect the choices of the majority.

In wake of Allied victory, a patriotic American economist named Kenneth Arrow felt that democracy had shown itself to be the worlds greatest system of government, and he wanted to prove it once and for all. With this goal in mind, he sat down and laid out the electoral process on paper using graphs and charts. What he found shocked him, and ultimately earned him a Nobel Prize. Take a look at the image below

http://htmlimg2.scribdassets.com/3o4mqhzvnk2fixtp/images/2-5e69df3bfa.jpg

When examining the way people vote, no matter how many candidates or voters are taking part in an election, Arrow found that the end result was always a giant game of rock paper scissors. In mainstream politics, it is assumed that the winner of an election is the candidate who the majority of people really wanted to hold office. But this is never (very rarely) the case. The way that modern elections in Western nations are set up is typically similar to a tournament bracket, with people moving further and further towards the final election between two people. But when Arrow took the winner of an election and put them up against someone who had already lost earlier in the campaigning season, he found that the newly elected politician would have ended up losing. The only thing that matters in an election is the order in which candidates face each other. However, it is true that it is possible to have what is known as a Condorcet Winner, someone who will win an election no matter how the election is arranged. An instance such as this is unbelievably rare, and the only one I can think off of the top of my head is Adolf Hitler.

As an anecdote, one of Arrow's students used this new discovery to his advantage. The young pupil was an avid pilot, and had recently become president of a flying club. The members of this club decided they were going to pool together some money to buy a plane, which they would then share the use of. But when the question of which plane they should buy arose, everyone had a different opinion. So Arrow's student had an idea, and told the club that he would set up an election to see which plane the club should buy. Of course, everyone agreed, as surely a fair election would reveal which aircraft the club ultimately wanted.

When Arrow's student was preparing to set up the election, he called each member of the flying club and asked them to rank their choices of aircraft so that he could get a feel for where everyone was at. Each member easily replied, saying things such as, "I would like a Cessna the most, but if not a Cessna then I'd take a Piper, then a Beechcraft, etc.." He wrote down what each member said until he had a list of preferred aircraft from everyone. He then took this knowledge and set up the election order so that the aircraft he wanted won. Kind of a dirty move you might think, but it's really no different than if he set up the election in another order. The results would have been random, he just made them random in his favor.

There are other curious things that happen in elections when groups of people vote that would normally seem insane if an individual did the same thing. For example, let's say it's a hot day and you feel like having some ice cream. So you walk into the ice cream shop and the owner says, "We have chocolate and vanilla ice cream, what would you like?" So you say, "Hmm.. I think I'll have vanilla." As the owner reaches down to scoop your ice cream, he stops and says, "Oh wait! I forgot! We also have strawberry!" To this you respond, "Oh, in that case I'll have chocolate ice cream." Now if someone did this, you would think they're crazy, or at least weird. Why would someone who wants vanilla over chocolate suddenly want chocolate over vanilla if strawberry becomes a choice? Well such decisions happens quite frequently in elections today.

I'll give a recent and real example to explain this one. In Virginia's last gubernatorial election, we had a Democratic candidate, Terry McAuliffe, and a Republican candidate, Ken Cuccinelli. Now, election polls and predictions were favoring Cuccinelli over McAuliffe, but then a third independent candidate was introduced, Robert Sarvis, and he took enough votes away from Cuccinelli to cause McAuliffe to win. This is the same situation as the ice cream shop. Decisions that are regarded as insane when individuals make them are a regular occurrence in groups.

Such elections are constantly happening today. For me, this begs the question, "Why have democracy?" Our system of choosing leaders is just as arbitrary as having a king or dictator, the only difference is that our politicians spend all of their time worrying about staying in office and preparing for the next campaigns, which causes them to worry only about what's going to benefit themselves in the short run, and not society in the long run. Democracy has also caused our governments to be made up of too many different people to effectively and quickly make decisions. It has caused Western societies to slowly degenerate to the point where there is almost no turning back.

Just some food for thought.






Further reading on the concepts:
http://www.academia.edu/3474379/Impossible_or_Arbitrary_-_How_the_Condorcet_Paradox_and_Arrows_Theorem_teac h_us_to_question_democratic_outcomes

http://faculty.georgetown.edu/kingch/Condorcet'sParadoxandArrow'stheoremoverhead.pdf

http://www.sjsu.edu/faculty/watkins/arrow.htm

[Aviator]

Bump for people who are disinterested in constant mudslinging.

[Aviator]

Final bump.

[arcticwolf]

If democracy is so bad why does it work so well in Switzerland?
Democracy is not a problem, is the quality of the population of a given country that is.

Garbage in, garbage out.

Any form of tyranny is trash. Maintain intelligent, self motivated, ethically healthy society, and there is nothing better than democracy.

Democracy fails, when society is demoralized and corrupted.

[Sveta]

If democracy is so bad why does it work so well in Switzerland?
Democracy is not a problem, is the quality of the population of a given country that is.

Garbage in, garbage out.

Any form of tyranny is trash. Maintain intelligent, self motivated, ethically healthy society, and there is nothing better than democracy.

Democracy fails, when society is demoralized and corrupted.

So you say that a majority of intelligent, self motivated, ethically healthy A people gaining power and dominance over likewise B people is an awesome thing?

[Ars Moriendi]

It's interesting. I guess it does confirm something that people must have detected by sheer intuition by now: Democratic elections are a process where the options are pre-selected and where the mediatic process for the most part dictates the outcomes. The most important things always stay out of the voters' grasp.

Yet it's convenient to have it. Republicanism is the best way to hide, or at least give make up change to, oligarchical rule.

[Prisoner Of Ice]

I didn't read the whole thing but that is why you should have a priority lisdting for votes. So if there's 30 candidates you can rank them in order of choice, which is like having automatic runnofs.

So one guy can choose.

1. Libertarian Party
2. Anarchist
3. Democrat

and someone else can choose

1. Tea Party
2. Republican

Etc.

This is simple way to solve the issue of parties presenting false dichotomies. But the politicians don't want this as it forces them to be less corrupt.

[LightHouse89]

I told you it is just an irrational system for large scale societies. I still believe citizens are entitled to certain rights however I believe in military or social service is the only way someone deserves a right to vote on anything or be a politician to begin with. This current system is irrational and makes me laugh....I mean just look at voter fraud, the electoral college etc.....the last mentioned even makes me question democracy even more. This is why I believe in National Socialism. The state ran everything....the economy never crashed either....today we rely on wall street and big banks..if they fall then everything we worked for goes with it. It is just an irrational system that doesnt make any sense.

[Anglojew]

http://izquotes.com/quotes-pictures/quote-it-has-been-said-that-democracy-is-the-worst-form-of-government-except-all-the-others-that-have-winston-churchill-37200.jpg

[LightHouse89]

If democracy is so bad why does it work so well in Switzerland?
Democracy is not a problem, is the quality of the population of a given country that is.

Garbage in, garbage out.

Any form of tyranny is trash. Maintain intelligent, self motivated, ethically healthy society, and there is nothing better than democracy.

Democracy fails, when society is demoralized and corrupted.

Mainly because Switzerland is a smaller country. It would most likely fall apart without a democracy. Smaller scale soceities can easily work with real democracy...unlike bigger super powers [fake democracies] which are ran by corporations, banks and other foreign big shot investing agendas......the fact is we are idiots to think we even live in a Democracy. I laugh when people tell me how wonderful it is. I mean its foolish to think that under this system industry etc will come back. It wont! America is not ran by the people as in the peasantry and it would be absurd to think it is. A country with this much power and influence in the world most certainly is not ran by 'the people' aka peasants....no way would the powers at be allow peasants a right to rule their kingdom of monopoly.

[Anglojew]

http://quotes.lifehack.org/media/quotes/quote-Winston-Churchill-the-best-argument-against-democracy-is-a-88536.png

[Aviator]

If democracy is so bad why does it work so well in Switzerland?
Democracy is not a problem, is the quality of the population of a given country that is.

Garbage in, garbage out.

Any form of tyranny is trash. Maintain intelligent, self motivated, ethically healthy society, and there is nothing better than democracy.

Democracy fails, when society is demoralized and corrupted.


I won't argue with you there. Nonetheless, these are fundamental and completely factual issues with democracy.

[Prisoner Of Ice]

Also a lot of things can't be left up to the whim of the day, like immigration and going to war. It needs to be set in the constitution that there are large limits on war or any kind of use of force. That has been abrograted in the US constitution, but a new constitution could help with these issues.

[Aviator]

Bump in hopes of sparking up more intellectual discussion in light of the constant trolling going on right now.

[LightHouse89]

I just view it as an irrational belief system, a complete fallacy. I mean in smaller scale societies it works but not for world powers....it only serves corporations and banking systems.....I mean just look at the influence lobbies have in Washington....how can you tell me democracy is even real anymore. I prefer Fascism. I am not trolling. For a time I believed in democracy until recent years I have become convinced it is the worst leadership for mankind.

[LightHouse89]

http://izquotes.com/quotes-pictures/quote-it-has-been-said-that-democracy-is-the-worst-form-of-government-except-all-the-others-that-have-winston-churchill-37200.jpg

But they were not tried.....just beaten into submission by democracy. I really believe democracy just by judging america is a total fallacy.

[Apis]

Democracy is inherently flawed; voting trends towards a two-party system, and the prospect of election is directly related to campaign funding. The latter leads to bias towards benefactors, who more often than not are in the form of corporate lobbyists. As mentioned by OP, elected leaders also tend to be more focused on actions that promote re-election, rather than benefit society. The only major advantage is that tyranny is non-existent. The primary issue, however, is finding a viable alternative.

[Anglojew]

But they were not tried.....just beaten into submission by democracy. I really believe democracy just by judging america is a total fallacy.

Which system do you prefer?

[Kale]

Yeah, democracy and capitalism are incompatible.

[LightHouse89]

I won't argue with you there. Nonetheless, these are fundamental and completely factual issues with democracy.

However the population is indoctrinated to be as stupid as they are today. There is nothing revolutionary about democracy anymore. Democracy has failed its intended purpose.

[LightHouse89]

Yeah, democracy and capitalism are incompatible.

What? They are inseparable.

[LightHouse89]

Which system do you prefer?

Fascism. It is the only thing that can help mankind as a whole. Democracy is a total fallacy. I mean it is absurd my politicians can accept bribes to push political agendas yet stand and claim they represent us when they totally do not.

[LightHouse89]

Democracy is inherently flawed; voting trends towards a two-party system, and the prospect of election is directly related to campaign funding. The latter leads to bias towards benefactors, who more often than not are in the form of corporate lobbyists. As mentioned by OP, elected leaders also tend to be more focused on actions that promote re-election, rather than benefit society. The only major advantage is that tyranny is non-existent. The primary issue, however, is finding a viable alternative.

Yes. So why bother having it? It failed itself. Its own fundamental beliefs come into question. Fascism is the future for mankind as a whole.

[Kale]

What? They are inseparable.

I could be the greatest person who ever lived. 50 feet tall, immortal, and can shoot unlimited quantities of sausage out of my eyes. But if I have no money (which translates into media exposure), who's going to know I even exist...let alone are going to cast their vote for me in an election.

[Aviator]

A random bump for new members or anyone who may be interested.

[LightHouse89]

bump

[Der Kampf]

Democracy as it exists now is a passive, incidental process of back-and-forth between political organisations that are essentially the same thing. Liberals will argue that democracy empowers the voter to have a direct say in how society is governed, but studies have shown that the chance of your individual vote having any quantifiable affect on the result of an election is negligible -- So even by it's own standards, democracy does not succeed. It is ostensibly a charade; it is the illusion of participation. Why is that? Well, it's because the system as it exists fulfils the necessary role of maintaining the status quo, or as liberals like to term it "stability" -- a sinister euphemism if ever I've heard one.

The farce of parliamentary democracy therefore highlights what I consider to be a more important question than whether democracy is "good" or "bad," namely: What is the purpose and role of a citizen? Because of the desperately pathetic political imagination of liberals and their quest to maintain secure political ground for the continued existence of capitalism, the citizen is reduced to a consumerist first and foremost, and secondly a passive observer of a political institution it has a nominal say in electing.

Well, in my view this is not what a citizen should be, nor should its role be to simply earn a wage, to disseminate that wage and nominally participate in an inconsequential political process. The purpose of a citizen is to build a national community, to be part of that community and to strive for its perseverance, protection and progress. Their role in that respect is to work for the good of the community, both economically and culturally, to defend the state and pursue its objectives, and to perpetuate the existence of that community through their role as parents.

When citizens have the responsibility and aspiration of building a community, working land and helping to benefit that community, within a national framework that ensures the work that is done is for the good of all; for the family, for the community and for the nation, and not for individual profit,, happiness, contentedness is established. It creates aspiration and it creates a unity amongst people. Happiness can only be found in that unity, in that hard work and in that collective responsibility to the nation.

How is this society structured then? Well, to create a nation state in this way negates the need for democracy as conceived by the liberals. It serves no purpose. The existence of a plethora of political parties vying for their own interests is antithetical to the establishment of a society predicated on a unity of purpose. No political interest is more important than the collective duty of a citizen to work for the betterment of their community, their people and their nation. It is a dangerous moralism that says otherwise and it should be ruthlessly opposed.

[Aviator]

Democracy as it exists now is a passive, incidental process of back-and-forth between political organisations that are essentially the same thing. Liberals will argue that democracy empowers the voter to have a direct say in how society is governed, but studies have shown that the chance of your individual vote having any quantifiable affect on the result of an election is negligible -- So even by it's own standards, democracy does not succeed. It is ostensibly a charade; it is the illusion of participation. Why is that? Well, it's because the system as it exists fulfils the necessary role of maintaining the status quo, or as liberals like to term it "stability" -- a sinister euphemism if ever I've heard one.

Thanks for actually contributing, and for being well-written.


"Well, in my view this is not what a citizen should be, nor should its role be to simply earn a wage, to disseminate that wage and nominally participate in an inconsequential political process. The purpose of a citizen is to build a national community, to be part of that community and to strive for its perseverance, protection and progress. Their role in that respect is to work for the good of the community, both economically and culturally, to defend the state and pursue its objectives, and to perpetuate the existence of that community through their role as parents."

I especially agree with this part. This is basically the opposite of what happens in the US, and I imagine many places in Europe now. Hopefully our societies will operate in this manner in the future...

[TLevin]

Fascism. It is the only thing that can help mankind as a whole. Democracy is a total fallacy. I mean it is absurd my politicians can accept bribes to push political agendas yet stand and claim they represent us when they totally do not.

Fascism is a form of democracy (or rather demoticism, leftism, identitarianism).

[Harris]

A random bump for new members or anyone who may be interested.

The problem with democracy is that only two types of people turn up to vote - outright ignoramuses or close-minded ideologues. No system built atop irrationality can survive or thrive, which is why democracy is and has always been heavily restricted in the West with a system of checks and balances, for example a written or unwritten constitution representing a supreme law. Direct democracy would be an unmitigated disaster.

Democracy also tends to, rather easily, descend into an oligarchy or plutocracy, for obvious reasons. Again, a constitution can reduce the impact of (or delay) this process, but ultimately it cannot stop it.

[Aviator]

The problem with democracy is that only two types of people turn up to vote - outright ignoramuses or close-minded ideologues. No system built atop irrationality can survive or thrive, which is why democracy is and has always been heavily restricted in the West with a system of checks and balances, for example a written or unwritten constitution representing a supreme law. Direct democracy would be an unmitigated disaster.

Democracy also tends to, rather easily, descend into an oligarchy or plutocracy, for obvious reasons. Again, a constitution can reduce the impact of (or delay) this process, but ultimately it cannot stop it.

All fair points, but even if you were to eliminate all of the problems you mentioned, you still wouldn't have alleviated the problems outlined in this topic. The winners of elections would still just arbitrarily come out on top based on the order that other candidates were eliminated from running.

[Harris]

All fair points, but even if you were to eliminate all of the problems you mentioned, you still wouldn't have alleviated the problems outlined in this topic. The winners of elections would still just arbitrarily come out on top based on the order that other candidates were eliminated from running.

I don't see how this response follows from what I posted? I wasn't addressing the OP directly, but rather (tangentially) some general issues with democracy. You can't "eliminate" the problems I outlined. They are inherent to democracy. Voters are neither informed nor rational, and democracy is far too fluid and anarchic to prevent oligarchical rule (to varying degrees).

But yes, it's pretty obvious that majority wishes can be in conflict with one another. Collective choices can be wholly irrational, which is why arguments supporting democracy that hinge on its supposed 'fairness' are deeply flawed.

[Aviator]

I don't see how this response follows from what I posted? I wasn't addressing the OP directly, but rather (tangentially) some general issues with democracy. You can't "eliminate" the problems I outlined. They are inherent to democracy. Voters are neither informed nor rational, and democracy is far too fluid and anarchic to prevent oligarchical rule (to varying degrees).

But yes, it's pretty obvious that majority wishes can be in conflict with one another. Collective choices can be wholly irrational, which is why arguments supporting democracy that hinge on its supposed 'fairness' are deeply flawed.

Ah, fair enough. I thought you were getting at something else entirely; I may have been drunk at the time.

In any case, I think it's time we move away from this failed experiment.

[Harris]

In any case, I think it's time we move away from this failed experiment.

In which direction should 'we' (the U.S I presume?) move? Towards a more centralised, stronger State where a single-party has total supremacy? I think that would be fiercely resisted by most Americans, who view duh big guvmentz as evil. Perhaps we should move towards a more localised form of government within the framework of a constitutional monarchy, with the power exercised by the Monarch revised to its post-Glorious Revolution days? That's what I want over here. Now that could have worked well in the U.S. :lol:

If I was you, I'd blame much of modern American degeneracy on the inability of the Redcoats to extract and seduce enough settlers. A strong America under the Crown! Imagine that!

[Aviator]

In which direction should 'we' (the U.S I presume?) move? Towards a more centralised, stronger State where a single-party has total supremacy? I think that would be fiercely resisted by most Americans, who view duh big guvmentz as evil. Perhaps we should move towards a more localised form of government within the framework of a constitutional monarchy, with the power exercised by the Monarch revised to its post-Glorious Revolution days? That's what I want over here. Now that could have worked well in the U.S. :lol:

If I was you, I'd blame much of modern American degeneracy on the inability of the Redcoats to extract and seduce enough settlers. A strong America under the Crown! Imagine that!

By "we," I was referring to Western nations in general.. I don't know if the US can make any system functional at this point in time, given the makeup of our population and our culture (or lack thereof.)

It would be interesting to see an alternative history where Britain won the Revolution, reenforcing not only Monarchy, but European dominance around the world. It was so long ago though, it's hard to say how different things would be today.

[SupaThug]

I will never understand why do people like democracy so much...unfortunaly it is a crime to critize it.

[ShannonFlynn]

It is fact that democracy is the major constituent for social, political and economic development. It is considered as the backbone of the system, without which an effective running of system is impossible.

[Hong Key]

http://media-cache-ak0.pinimg.com/736x/70/2c/f0/702cf0f279f540ab2c74371c43c38b45.jpg

[Prisoner Of Ice]

All fair points, but even if you were to eliminate all of the problems you mentioned, you still wouldn't have alleviated the problems outlined in this topic. The winners of elections would still just arbitrarily come out on top based on the order that other candidates were eliminated from running.

There is no real problem, this is just basic math. It's not that they can't make fair elections that give smaller parties a fair chance, they don't want to.

[Aviator]

There is no real problem, this is just basic math. It's not that they can't make fair elections that give smaller parties a fair chance, they don't want to.

Even if they did want to, there's really just no way to set up an election that legitimately reflects the will of the people. No matter the outcome, a candidate who was knocked out earlier in the campaigning season will (virtually) always be able to beat whoever actually comes out on top.

Rock, paper, scissors. Which one is the true winner?