Why Democracy Is Mathematically Impossible

Summary

This video delves into the mathematical challenges of democracy, particularly in voting systems. It critiques the 'first past the post' method, highlighting its tendency to produce majority governments that don't reflect the majority's will. The script explores alternatives like instant runoff voting and points out its own paradoxes, such as how a poorly performing candidate can influence election outcomes. It introduces Arrow's Impossibility Theorem, which states that no ranked voting system can satisfy all desired fairness conditions, and contrasts it with Black's Median Voter Theorem, suggesting a more optimistic view of democratic voting. The video concludes by advocating for approval voting as a potentially fairer method and encourages political engagement despite the imperfections of the democratic process.

Takeaways

• 😀 Democracy's current voting methods are fundamentally irrational, leading to potential instability and misrepresentation.
• 🏛️ 'First past the post' voting, used by 44 countries, can result in parties gaining power without majority support, as seen in the UK's parliamentary history.
• 🗳️ The spoiler effect, as in the 2000 US presidential election, can lead to unintended election outcomes due to vote-splitting among similar parties.
• 🔄 'Instant runoff' or ranked-choice voting can mitigate the spoiler effect and encourage more cooperative candidate behavior, as demonstrated in the 2013 Minneapolis mayoral race.
• 🔢 Arrow's Impossibility Theorem states that no ranked voting system can satisfy five reasonable conditions simultaneously, suggesting inherent limitations in democratic voting systems.
• 🤔 Condorcet's method, which involves pairwise comparison of candidates, can result in paradoxes where cyclic preferences prevent a clear winner from emerging.
• 📊 Black's Median Voter Theorem offers a more optimistic view, suggesting that in one-dimensional political spectra, the preference of the median voter can determine the majority decision.
• 👍 Approval voting, an alternative to ranked voting, allows voters to express approval for one or more candidates and can increase voter turnout and reduce negative campaigning.
• 🏆 Approval voting has historical precedents, such as electing the Pope in the Vatican and the Secretary-General of the United Nations.
• 💡 Despite theoretical challenges, democracy remains the best form of government available, and engagement in the political process is crucial for making a difference.
• 🌐 The script concludes with a call to expand knowledge and critical thinking skills to better understand and participate in an ever-changing world.

Q & A

What is the main argument presented in the video about democracy and mathematics?

The video argues that the methods currently used to elect leaders in democratic societies are fundamentally irrational from a mathematical perspective, leading to potential instability and misrepresentation.

What is 'first past the post' voting and why does it have issues?

'First past the post' is a voting system where the candidate with the most votes wins. It has issues because it can lead to situations where the majority of the country did not vote for the party that ends up holding power, and it can cause similar parties to 'steal' votes from each other, leading to a two-party system.

What is the 'spoiler effect' in elections?

The 'spoiler effect' occurs when a candidate with similar views to another takes votes away, potentially causing the less preferred candidate to win. This effect discourages voters from voting for their true preference if it's not a leading contender.

What is the 'instant runoff' voting system and how does it work?

The 'instant runoff' voting system, also known as preferential or ranked-choice voting, allows voters to rank candidates by preference. If no candidate has a majority after the first count, the candidate with the fewest votes is eliminated, and their votes are redistributed according to the voters' second preferences, repeating this process until a candidate has a majority.

How does the 'instant runoff' system affect candidate behavior?

The 'instant runoff' system encourages candidates to be more cordial and polite to each other, as they are vying for second and third preferences from voters who support other candidates.

What is Arrow's Impossibility Theorem and what does it imply for voting systems?

Arrow's Impossibility Theorem states that it is impossible to create a ranked voting system that satisfies five reasonable conditions when there are three or more candidates. This implies that no voting system can perfectly and rationally aggregate voter preferences without some form of compromise.

What are the five conditions outlined by Kenneth Arrow for a fair voting system?

The five conditions are: Unanimity (if everyone prefers one option, the group should too), Non-dictatorship (no single vote should override all others), Unrestricted Domain (all voters can vote freely and the system must produce a conclusion), Transitivity (if the group prefers A over B and B over C, they should prefer A over C), and Independence of Irrelevant Alternatives (adding or removing a candidate should not affect the preference between two existing candidates).

What is Condorcet's method and how does it differ from other voting systems?

Condorcet's method is a voting system where the winner is the candidate who would win in a head-to-head election against every other candidate. It differs from other systems by focusing on pairwise comparisons of candidates rather than aggregating total points or votes.

What is Condorcet's Paradox and how does it challenge the fairness of voting systems?

Condorcet's Paradox occurs when there is a circular preference among three or more options, where each option is preferred to the next and the last is preferred to the first, creating a logical loop with no clear winner. This paradox challenges the idea that a voting system can always produce a fair and consistent outcome.

What alternative voting system is suggested in the video as a potential solution to the issues with ranked voting?

The video suggests rated voting systems, such as approval voting, as a potential solution. In approval voting, voters indicate which candidates they approve of, and the candidate with the highest approval wins, which can increase voter turnout and decrease negative campaigning.

Outlines

00:00

🗳️ The Impossibility of Perfect Democracy

The script discusses the inherent mathematical challenges in achieving a perfect democratic voting system. It begins by critiquing the 'first past the post' voting method, which has historically led to situations where the majority's choice does not align with the ruling party. The script also touches on the 'spoiler effect' as seen in the 2000 US presidential election, where third-party candidates can inadvertently influence the outcome by splitting the vote. The discussion then shifts to alternative voting methods, such as 'instant runoff' or ranked-choice voting, which aim to address some of these issues but are not without their own complexities and potential for paradoxical outcomes.

05:03

🔄 The Evolution of Voting Systems

This section delves into the evolution of voting systems, from the Condorcet method to the Borda count, each with its own set of advantages and disadvantages. The Condorcet method, which involves pairwise comparison of candidates, is highlighted for its potential to determine a consensus candidate, yet it is also shown to be susceptible to paradoxes. Borda's system, which assigns points based on rankings, is criticized for being influenced by the number of candidates, which can lead to irrelevant factors affecting the outcome. The script also introduces the work of mathematicians like Charles Dodgson (Lewis Carroll) and Kenneth Arrow, who contributed to the understanding of voting systems and the inherent impossibilities within them.

10:04

🤔 Arrow's Impossibility Theorem

The script presents Kenneth Arrow's seminal work, the Impossibility Theorem, which states that it is impossible to create a ranked voting system that satisfies five reasonable conditions when there are three or more candidates. These conditions include unanimity, non-dictatorship, unrestricted domain, transitivity, and independence of irrelevant alternatives. The theorem is illustrated through a thought experiment involving voters' preferences for candidates, demonstrating that any such system will inevitably lead to a dictatorial influence on the outcome, thus challenging the very concept of democratic decision-making.

15:04

📊 Alternative Voting Systems and Their Impact

The script explores alternative voting systems, such as approval voting, which allows voters to express approval for multiple candidates rather than ranking them. This method is shown to have potential benefits, including increased voter turnout, reduced negative campaigning, and the prevention of the spoiler effect. It also touches on the historical use of approval voting in the Vatican and for electing the UN Secretary-General. The discussion highlights the need for further real-world testing of these systems to better understand their effectiveness in large-scale elections.

20:04

🌐 The Imperfections of Democracy and the Importance of Engagement

In the final paragraph, the script acknowledges the imperfections of democracy but emphasizes its value as the best form of government available, as famously stated by Winston Churchill. It encourages viewers to stay politically engaged and to continuously expand their knowledge and critical thinking skills to adapt to a changing world. The script concludes with a sponsorship message for Brilliant, an educational platform that offers courses in various subjects, including probability and statistics, to help viewers become better thinkers and problem solvers.

Keywords

💡Democracy

Democracy refers to a system of government where power is vested in the people and exercised by them directly or through elected representatives. In the context of the video, it is discussed in relation to the challenges of achieving a fair and rational democratic process through voting systems. The script mentions that despite being a fundamental aspect of civilization, the methods currently used to elect leaders may not be the most rational, hinting at the mathematical impossibility of perfect democracy.

💡First Past the Post

First Past the Post (FPTP) is an electoral system where the candidate with the most votes in a constituency wins, regardless of whether they have the majority. The video script uses this term to illustrate a common voting method that has been historically used but is criticized for not always reflecting the will of the majority, as it can lead to a party gaining power without the majority of the votes.

💡Spoiler Effect

The Spoiler Effect occurs in an election when a candidate with similar policies to another takes votes away, potentially causing the less popular candidate to win. The script references the 2000 US Presidential Election, where Ralph Nader's candidacy is suggested to have split the vote, possibly influencing the election outcome in favor of George W. Bush.

💡Strategic Voting

Strategic Voting is when voters choose not to vote for their preferred candidate but for another who they believe has a better chance of winning. The video discusses how First Past the Post incentivizes this behavior, as voters may opt for a more popular candidate to prevent their least favorite from winning, rather than voting for their true preference.

💡Instant Runoff

Instant Runoff Voting (IRV) is a voting system where voters rank candidates by preference. If no candidate has a majority of the first-preference votes, the candidate with the fewest votes is eliminated, and their votes are redistributed based on the voters' next preferences. The video explains how IRV can change candidate behavior, encouraging politeness and cooperation to secure second or third preferences.

💡Condorcet's Paradox

Condorcet's Paradox occurs when, in a ranked voting system, no candidate can be said to be the majority's choice when compared head-to-head against all other candidates. The video uses the example of a dinner choice between burgers, pizza, and sushi, where a circular preference among the options leads to no clear winner, illustrating the paradox.

💡Arrow's Impossibility Theorem

Arrow's Impossibility Theorem, proposed by economist Kenneth Arrow, states that it is impossible to create a ranked voting system that satisfies certain fair criteria when there are three or more candidates. The video script explains this theorem as a mathematical fact that challenges the idea of a perfect democratic voting system, as no method can satisfy all the conditions of fairness without leading to paradoxes or inconsistencies.

💡Median Voter Theorem

The Median Voter Theorem suggests that in a one-dimensional voting model, the policy preferred by the median voter will be chosen in a majority-rule election. The video script mentions this theorem as a more optimistic perspective on democracy, suggesting that the preferences of the majority can still be reflected in the outcome, despite the impossibility theorem.

💡Approval Voting

Approval Voting is a type of voting system where voters can vote for as many candidates as they approve of, rather than ranking them. The video suggests that this system can increase voter turnout, decrease negative campaigning, and prevent the spoiler effect, as it allows voters to express approval without strategic considerations.

💡Independence of Irrelevant Alternatives

The Independence of Irrelevant Alternatives is one of Arrow's conditions for a fair voting system, stating that the addition or removal of an option that is not the first choice of any voter should not affect the outcome of the election. The video script discusses how this condition, along with others, cannot all be satisfied simultaneously in a ranked voting system with three or more candidates.

Highlights

Democracy's methods of electing leaders are fundamentally irrational, a mathematical fact that led to a Nobel Prize.

First-past-the-post voting, used in 44 countries, can lead to parties with minority votes holding power.

The spoiler effect in first-past-the-post voting can result in the election of a less preferred candidate.

Strategic voting in first-past-the-post systems can concentrate power in larger parties, leading to a two-party system.

Instant runoff voting, or ranked-choice voting, saves time by eliminating the need for multiple elections.

Candidates in ranked-choice voting systems tend to be more cordial to secure second and third preferences.

Instant runoff voting can paradoxically elect a candidate despite them performing worse initially.

Condorcet's method, proposed by the French mathematician, aims to find the most fair voting system.

Condorcet's paradox shows that a voting system can end in a loop with no clear winner.

Arrow's impossibility theorem states that it's impossible to satisfy five reasonable conditions in a ranked voting system with three or more candidates.

Duncan Black's theorem offers a more optimistic view of democracy, suggesting the preference of the median voter reflects the majority.

Rated voting systems, like approval voting, can increase voter turnout and decrease negative campaigning.

Approval voting prevents the spoiler effect and allows voters to express approval without strategic concerns.

Arrow initially doubted rated voting systems but later acknowledged their potential as the best method.

Democracy, despite its flaws, is the best form of government compared to all other forms tried.

Expanding knowledge and critical thinking skills is crucial for adapting to the changing world.

Brilliant.org is highlighted as a tool for daily learning and critical thinking skill development.

Transcripts

democracy might be mathematically impossible  this isn't a value judgment a comment about  

human nature nor a statement about how rare and  unstable Democratic societies have been in the  

history of civilization our current attempt  at democracy the methods we're using to elect  

our leaders are fundamentally irrational and  this is a well-established mathematical fact  

this is a video about the math that proved  that fact and led to a Nobel Prize it's a  

video about how groups of people make decisions  and the pitfalls that our voting systems fall

into one of the simplest ways to hold an election  is to ask the voters to mark one candidate as  

their favorite on a ballot and when the votes  are counted the candidate with the most votes  

wins the election this is known as first past the  post voting the name is kind of a misnomer though  

there is no post that any of the candidates need  to get past. the winner is just the candidate with  

the most votes this method likely goes back to  Antiquity it has been used to elect members of  

the House of Commons in England since the 14th  century and it's still a common voting system  

with 44 countries in the world using it to elect  its leaders 30 of these countries were former  

British colonies the us being a former British  colony still uses first past the post in most  

of its states to elect their representatives to  the electoral college but first pass the post has  

problems if you are selecting representatives  in a parliament you can and frequently do get  

situations where the majority of the country did  not vote for the party that ends up holding the  

power in the last 100 years there were 21 times a  single party held a majority of the seats in the  

British Parliament but only two of those times  did the majority of the voters actually vote for  

that party so a party which only a minority of  the people voted for ends up holding all of the  

power in government another thing that happens  because of first pass the post is that similar  

parties end up stealing votes from each other  the 2000 US presidential election which was an  

election essentially between Al Gore and George W  bush at that point every state in the nation used  

first pass the post to determine the outcome of  the election bush had more votes in Florida but  

by a ridiculously slim margin it was fewer than  600 votes but there was another candidate on the  

ballot Ralph Nader. Nader was a green candidate he  was certainly to the left of either Gore or bush  

what we need is the upsurge of Citizen concern  people concerned poor Rich or middle class to  

counteract the power of the special interest  and he got almost 100,000 votes in Florida I  

just don't know if I can with a conscience um  vote for uh Bush or Gore I will vote for Ralph  

Nader most of those voters were devastated that  by voting for Nader rather than Gore they ended  

up electing Bush This is what is called a spoiler  effect almost all Nader voters preferred Gore  

to Bush but in a first pass post system they had  no way of expressing that preference because you  

could only vote for one candidate so first pass  the post incentivizes voters to vote strategically  

say there are five parties one of them will be  the smallest one and so they won't win why would  

you vote for them this is also true if you have  four parties or three parties this Winner Takes  

all voting system leads to a concentration of  power in larger parties eventually leading to  

a two party system this effect is common  enough that it has a name do verger's

law so first pass the post isn't a great option  so what else could we do well we can say that a  

candidate can only win an election if they get  a majority at least 50% plus one of the vote  

but what if we hold an election and no one gets  a majority we could go to the people who voted  

for the candidate with the fewest votes and ask  ask them to vote again but choose a different  

candidate and we could repeat this process over  and over eliminating the smallest candidate until  

one candidate reaches a majority but holding many  elections is a big hassle so instead we could just  

ask voters to rank their preferences from their  favorite to their least favorite and if their  

favorite candidate gets eliminated we go to their  second preferences when the polls close you count  

the voters first choices if any c cidate has a  majority of the votes then they're the winner but  

If no candidate has a majority the candidate with  the fewest votes gets eliminated and their ballots  

are distributed to those voters second preferences  and this keeps happening until one candidate has  

a majority of the votes this is mathematically  identical to holding repeated elections it just  

saves the time and hassle so it's referred to  as instant runoff but the system is also known  

as preferential voting or ranked Choice voting an  instant runoff doesn't just affect the voters it  

affects how the candidates behave towards each  other it was the Minneapolis mayor's race 2013  

they were using rank Choice voting the incumbent  mayor had stepped down and there were all of these  

people came out from the woodwork wanting to be  mayor there 35 candidates and so you would think  

if there's 35 candidates you'd want to dunk on  someone you'd want to like kind of elbow yourself  

into the spotlight that's not what happened  these 35 candidates all of them were really  

nice to each other they were all super cordial  super polite to the degree that at the end of the  

final mayoral debate they all came together  and they sang Kumbaya together k k oh Lord

the amount of vitriol and anger and partisan  you know mudslinging that we're all used to to  

see this vision of an actual Kumbaya it's not  even a joke all of these people getting along  

so desperate for second and third choices from  other people that they're like I'm going to be  

the picture perfect kindest candidate possible  but there's also a problem with instant runoff  

there can be cases where a candidate doing worse  can actually help help get them elected let's say  

we have three candidates Einstein curee and bore  now Einstein and bore have very conflicting views  

while C is ideologically in the center so let's  say Einstein gets 25% of the vote cirri gets 30  

and bore gets 45 no one got a majority so  it goes to the second round with Einstein  

being eliminated and because people who voted for  Einstein put down c as their second choice well  

C ultimately gets elected but now imagine that  bour has a terrible campaign speech or proposes  

a very unpopular policy so bad that some of his  voters actually switch over to Einstein's side  

well now it's curee that gets eliminated  and because she's more moderate half of  

her voters select Einstein and the other half  select bore in the second round and this leads  

to boore winning so bore doing work in the first  round actually leads to him winning the election  

clearly this isn't something that we want  in a voting system this is what the french  

mathematician Condor also thought Condor  was one of the first people applying logic  

and Mathematics to rigorously study voting  systems making him one of the founders of a  

branch of mathematics known as social Choice  theory he was working during the time of the  

French Revolution so fairly determining the will  of the people was having a cultural moment right

then in 1784 condor's contemporary at the French  Royal Society of science Jean Charles de borda  

proposed a voting method you ask the voters to  rank the candidates if there are five candidates  

ranking someone first gives that candidate Four  Points ranking them second would give them three  

and so on with zero points being awarded for last  place but the board account has a problem because  

the number of points given to each candidate  is dependent on the total number of candidates  

adding extra people that have no chance of winning  can affect the winner because of this condr hated  

Border's idea he wrote that it was bound to lead  to error because it relies on irrelevant factors  

for its judgments so in 1785 Condor published an  essay in which he proposed a new voting system  

one he thought was the most Fair basically the  winner needs to beat every other candidate in  

a head-to-head election but with more than two  candidates do you need to hold a large number of  

head-to-head elections to pick the winner well no  just ask the voters to rank their preferences just  

like in instant runoff and then count how many  voters rank each candidate higher than each other  

candidate this feels like the most Fair voting  [Music] method this voting system was actually  

discovered 450 years earlier by Raymond lull a  monk who was looking at how church leaders were  

chosen but L's ideas didn't make an impact because  his book ours electionus the art of Elections was  

lost and only rediscovered in 2001 so the voting  system is named after cond and not lol but will  

there always be a winner in this way let's try  condor's method for choosing dinner between you  

and two friends there are three options burgers  pizza or sushi you really like burgers so that's  

your first preference your second choice is pizza  and you put Sushi last your friend prefers pizza  

then Sushi then burgers and your other friend  prefers Sushi than Burgers then pizza now if  

you choose Burgers it can be argued that Sushi  should have won instead since two of you prefer  

Sushi over burgers and only one prefers Burgers  to Sushi however by the same argument Pizza is  

preferred to Sushi and burgers are preferred to  Pizza by a margin of 2: one on each occasion so  

it seems like you and your friends are stuck in  a loop burgers are preferred to Pizza which is  

preferred to Sushi which is preferred to Burgers  and so on this situation is known as condor's  

Paradox Condor died before he could resolve  this problem with his voting system he was  

politically active during the French Revolution  writing a draft of France's Constitution in 1793  

during the reign of terror when Le monang came to  power he was deemed a traitor for criticizing the  

regime specifically their new constitution  the next year he was arrested and died in

jail over the next 150 years dozens of  mathematicians were proposing their own  

voting systems or modifications to Condor  or bord ideas one of those mathematicians  

was Charles Dodson better known as Lewis Carroll  when he wasn't writing Alice in Wonderland he was  

trying to find a system to hold Fair elections but  every voting system had similar kinds of problems  

you'd either get Condor Loops or other candidates  that had no chance of winning would affect the  

outcome of the election in 1951 Kenneth Arrow  published his PhD thesis and in it he outlined  

five very obvious and reasonable conditions  that AR voting system should have condition  

number one if everyone in the group chooses one  option over another the outcome should reflect  

that if every individual in the group prefers to  eat sushi over pizza then the group as a whole  

should prefer Sushi over Pizza this is known as  unanimity condition two no single person's vote  

should override the preferences of everyone else  if everyone votes for pizza except one person who  

votes for sushi the group should obviously choose  Pizza if a single vote is decisive that's not a  

democracy that's a dictatorship condition three  everyone should be able to vote however they want  

and the voting system must produce a conclusion  for society based on all the ballots every time  

it can't avoid problematic ballots or candidates  by simply ignoring them or just guessing randomly  

it must reach the same answer for the same set  of ballots every time this is called unrestricted  

domain condition four the voting system should  be transitive if a group prefers Burgers over  

pizza and pizza over Sushi then they should  also prefer Burgers over Sushi this is known  

as transitivity condition five if the preference  of the group is Sushi over Pizza the introduction  

of another option like burgers should not change  that preference sure the group might collectively  

rank Burgers above both or in the middle or at  the bottom but the ranking of sushi over Pizza  

should not be affected by the new option this is  called the independence of irrelevant Alternatives  

but here's the thing Arrow proved that satisfying  all five of these conditions in a ranked voting  

system with three or more candidates is impossible  this is Arrow's impossibility theorem and it was  

so groundbreaking that Arrow was awarded the Nobel  prize in economics in 1972 so I want to go through  

a version of his proof based on a formulation by  GN acus so let's say there are three candidates  

running for election Aristotle bore and C but  we'll refer to them as a b and c and we have a  

collection of Voters that will line up in order  so we have voter 1 2 3 and so on all the way up  

to n each of these voters is free to rank a b and  c however they like I'll even allow ties now the  

first thing we want to show is that if everyone  ranks a particular candidate first or last then  

society as a whole must also rank that candidate  first or last let's arbitrarily pick candidate B  

if say half of the voters rank B first and half  rank B last then the claim is our voting system  

must put B either first or last and we'll prove  it by contradiction so say this is how everyone  

voted if our system does not put B first or last  but rather in the middle say a is ranked above  

B which is above C then we'll get a contradiction  because if each of our voters moved C above a then  

by unanimity C must be ranked above a however  because we didn't change the position of any a  

relative to B A must still be ranked above B  and because we didn't change the position of  

any c relative to B C must still be ranked below  B and by transitivity if a is preferred to B and  

B is preferred to C then a must be ranked above C  but this contradicts the result by unanimity and  

that proves that if everyone ranks a candidate  first or last then Society must also rank them  

first or last now let's do a thought experiment  where every voter puts B at the bottom of their  

ranking we leave the ranking of A and C arbitrary  well then by unanimity we know that b must be at  

the bottom of society's ranking we'll call this  setup profile 0 now we'll create profile one which  

is identical to profile Z except the first voter  moves B from the bottom to the top this of course  

doesn't affect the outcome but we can keep doing  this creating profiles 2 3 4 and so on with one  

more voter of clipping B from the bottom to the  top each time if we keep doing this there will  

eventually come a voter whose change from having  B at the bottom to B at the top will first flip  

society's ranking moving B to the top let's call  this voter the pivotal voter and we'll label the  

profile profile P profile o is then the profile  right before the pivotal change happens let's now  

create a profile Q which is the same as P except  the pivotal voter moves a above B by independence  

of irrelevant Alternatives the social rank must  also put a above B since for all of our voters  

the relative position of A and B is the same as  it was in profile O and B must be ranked above C  

because the relative positions of B and C are the  same as they were in profile P where our pivotal  

voter moved B to the Top by transitivity a must be  ranked above C in the social ranking this is true  

regardless of how any of the non-pivotal voters  rearrange their positions of A and C because  

these rearrangements don't change the position  of a relative to B or C relative to B this means  

the pivotal voter is actually a dictator for  determining society's preference of a over C the  

social rank will always agree with a pivotal voter  regardless of what the other voters do we can run  

a similar thought experiment where we put C at the  bottom and prove that there is again a dictator  

who in this case determines the social preference  of A over B and it turns out this voter is the  

same one who determines the social preference  for a over C the pivotal voter is therefore  

a complete dictator so is democracy doomed well  arrows impossibility theorem seems to say so if  

there are three or more candidates to choose from  there is no ranked Choice method to rationally  

aggregate voter preferences you always need to  give something [Music] up but the mathematician  

Duncan black found a much more optimistic theorem  which might actually represent reality better if  

voters and candidates are naturally spread along  a single Dimension say ranging from Liberal on  

the left to conservative on the right but this  could apply to any other political Dimension  

well then black showed that the preference of the  median voter will reflect the majority decision  

the median voters choice will often determine the  outcome of the election a result that aligns with  

the majority of Voters avoiding the paradoxes  and inconsistencies highlighted by arrow and  

there's more good news Arrow's impossibility  theorem only applies to ordinal voting systems  

ones in which the voters rank candidates over  others there is another way rated voting systems  

the simplest version is known as approval voting  where instead of ranking the candidates the voters  

just tick the candidates they approve of there  are also versions where you could indicate how  

strongly you like each candidate say from minus 10  strongly disapprove of to plus 10 strongly approve  

research has found that approval voting increases  voter turnout decreases negative campaigning and  

prevents the spoiler effect voters could express  their approval for a candidate without worrying  

about the size of the party they're voting for  it's also simple to tally just count up what  

percentage of the voters approve of each candidate  and the one with the highest approval wins Kenneth  

Arrow was initially skeptical of rated voting  systems but toward the end of his life he agreed  

that they were likely the best method approval  voting is not new it was used by priests in the  

Vatican to elect the pope between 1294 and  1621 it's also used to elect the Secretary  

General of the United Nations but it hasn't been  widely used in large scale elections and so more  

real real world testing is likely required so is  democracy mathematically impossible well yes if  

we use rank Choice methods of voting which  is what most countries in the world use to  

elect their leaders and some methods are clearly  better at aggregating the people's preferences  

than others the use of first past the post voting  feels quite frankly ridiculous to me given all of  

its flaws but just because things aren't perfect  doesn't mean we shouldn't try being interested in  

the world around us caring about issues and being  politically engaged is important it might be one  

of the few ways we can make a real difference in  the world like Winston Churchill said democracy  

is the worst form of government except for all the  other forms that have been tried democracy is not  

perfect but it's the best thing we've got the  game might be crooked but it's the only game in

town the world is changing how it works today is  no guarantee of how it'll work tomorrow from how  

we elect presidents to how we do our jobs luckily  there's an easy way to be ready for whatever the  

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