Don’t we love democracy?
Well, according to most of the Western world, there’s nothing better we could have than democracy. And, at first glance, I couldn’t agree more. When you look at history, when you look at communism, fascism, or even monarchism - it dawns on you how easy we have it; how grateful we should be for the gift that is democracy.
Democracy stems from the Greek word democratia, meaning ‘the rule of the people’. Thus, at its roots, democracy’s might is that it gives power to the people to decide their own politics.
You might think to yourself: “I don’t see any problem with that. What could possibly go wrong?” Well, it’s quite simple. Equally - if not more - important than the fundamentally good ideas it puts forward, is the implementation of democracy. Today, we’ll look at just that - we're looking at society’s backbone: Political Decision-Making Systems.
First and foremost, let’s observe the French voting system. As you may know, under the 5th Republic, the Presidential Election is carried out via a two-round uninominal election - meaning you can only vote for one candidate. This seems like a simple system, to the point where we can't see how it could, realistically, improve. And yet, we know that it possesses several flaws.
An adequate example is the 2002 French Presidential Election. Although one of the candidates - Lionel Jospin - was eliminated by a small margin in the 1st round, polls predicted he could very well have won against either of the other candidates, had he been part of the 2nd round.
Here’s where the weakness of this system arises: every time we have a candidate with a real chance of winning the election, a group of unpopular candidates with similar results take away votes that could have been decisive.
Now, this situation is not unique to France. In fact, it’s even worse in the US, with its mere 1 round of national voting.
Let’s take a sports analogy. Picture yourself in a race, where the slowest runners can hold back the fastest by tugging their shorts. In that case, the winner of the race wasn’t actually the fastest, but rather the runner who managed to be held back the least.
Now, I think we all agree that this is illogical and contrary to fair play and sportsmanship. And yet, this is exactly what happens at the presidential election. The outcome is decisively influenced by the presence or absence of certain smaller candidates. But we're talking about something far more important than the outcome of a race - we’re talking about the future of a country!
Let’s get things straight. We have a democracy, and we get to choose our leaders - that’s all fine and dandy. But the decision-making system we use is completely messed up.
Can't we find a different method that would avoid all these problems? A way of voting that would be fairer, more thorough, and more representative of the people. Well, believe it or not, that question has been studied by mathematicians and political scientists. And now, we can look at it through the eyes of science.
To avoid this kind of situation, in France or in the US, one solution would be to simply perform more rounds of voting. However, practically, this would be far too time-consuming.
Instead, there exists a solution to fix the problem in only 1 round of voting.
The idea is to ask the voters not to put only one name down, but to rank all the candidates by order of preference. With this technique, we can figure out the outcome of each round at once.
To simulate the 1st round of voting, we only look at who was ranked 1st on each ballot. We calculate the % of each candidate and we see who got last, before eliminating that name. To simulate the 2nd round, we again take the 1st choice on each ballot, except for those who ranked the eliminated candidate as their 1st choice. For them, we take the 2nd choice from their list. Once again, we calculate the % of each candidate and get rid of the last one.
We repeat this process until we have a winner.
This voting system truly exists: it's called "Alternative Voting", or “Instant-Runoff Voting”. The superiority of this method lies in the fact that we can better express people's true opinions.
The problem with the uninominal voting system is that we reduce all our complex opinions to the choice of merely one name.
You might be thinking: “Is Alternative Voting the way to go?”. Well, it turns out that other issues arise. Usually, we know what candidates we like and those we dislike. However, ranking a multitude of candidates in a meaningful way isn’t that simple for a voter.
Although this method allows us to rank the myriad of unpopular candidates as we find in France or the US, as soon as we get to the penultimate round, with only 3 candidates left, we find ourselves back in the regular situation of a 2 round election. Now, a peculiar mathematical phenomenon emerges in this situation.
Let’s imagine there are only 2 rounds left, with 3 candidates: John, Andew, and Emma.
Say, 34% ranked John before Andrew, and Andrew before Emma.
Then, 32% ranked Andrew before John, and John before Emma.
Finally, 34% ranked Emma before Andrew, and Andrew before John.
We simulate the 1st round. Everyone votes for their preferred candidates.
Thus, John has 34%, Emma 34% as well but Andrew only 32%, eliminating Andrew.
On to the 2nd round - those who voted for Andrew in the 1st round now find themselves with John. Hence, John gets 66% and Emma 34%. Meaning John wins by a landslide.
Let’s now consider that things didn't exactly pan out like that. What if John had a more effective campaign, and was able to snatch a mere 3% of Emma’s votes?
Then we would have the following percentages for the rankings:
John > Andrew > Emma : 37%
Andrew > John > Emma : still 32 %
and Emma > Andrew > John : 31%
Now we simulate the 1st round again: John 37%, Andrew 32%, and Emma 31%, eliminating Emma.
If we simulate the 2nd round, this time we end up with Andrew winning with 63% of the votes.
Does anyone see the paradox here?
In the 1st situation, John is elected, but if he gets simply 3% of the 1st round votes, he could end up losing! Once more, putting democracy in peril.
This exact phenomenon is known as "Arrow's Paradox". Whether in a classic or alternative system, as you progress in the rankings, your chance of winning could decline - which is absurd!
Besides its complete incoherence, this breeds the "strategic vote" - which is when we don't vote for the person we want to see win, but rather exploit the defects of the voting system to help our preferred candidate. Here is another paradox of the classic system. Let’s take our 3 candidates from earlier on once again.
Imagine voters rank them in the following ways:
40% prefer Andrew to John, and John to Emma.
40% prefer Emma to John, and John to Andrew.
10% prefer John to Andrew, and Andrew to Emma.
10% prefer John to Emma, and Emma to Andrew.
Let's simulate the 1st round. We take the 1st choice of each voter, meaning Andrew and Emma both get 40%, John gets only 20% and finds himself eliminated. Therefore, the 2nd round is between Andrew and Emma. And yet, if we had a duel between John and Andrew only, John would win 60-40. The same goes for a duel between John and Emma, he would also win. So John is capable of beating each opponent individually but is unable to access the final round. This makes no sense. In fact, this is not something new. It was actually noticed in 1785, by Nicolas de Condorcet - a French mathematician and philosopher who pioneered the scientific study of political decision-making systems. Based on his findings, Condorcet came up with his own voting system - called the Condorcet Method. The idea is simple enough: we organize electoral duels between each candidate and keep the one who can beat everyone else.
Seems like a good plan, right? Well, that’s not the case. Condorcet noticed that there are certain situations where no candidate is able to beat all of the others.
Let's take 3 candidates named A, B, and C.
Say 1/3 prefers A to B and B to C.
Another 1/3 prefers B to C and C to A.
And the last 1/3 prefers C to A and A to B.
If we have a duel between A and B - A wins.
If we have a duel between B and C - B wins.
In a duel between A and C - C wins. That means that no candidate can win all of his duels.
This is so strange, actually, that it is known as Condorcet's Paradox. A contemporary of Condorcet, Mr. Borda, proposed a variation to his method. Like in the "Alternative Vote", everybody ranks the candidates, and then we give them points accordingly. For example, 1 point for last place, 2 points for the second to last…and N points to the 1st place given N candidates. The winner, in this system, is the candidate with the most points. If we apply this to our example with Andrew, John, and Emma - we end up with 190pts for Andrew and Emma, and 220pts for John, who would win the election.
This seems perfect, doesn’t it? Well, as you might have guessed… this isn’t ideal either. Indeed, the system’s success depends on how you decide to distribute the points.
And, just like in a classic election, small candidates can have a decisive influence on the more popular candidates. Alright, this may seem a bit discouraging - we observed a couple of electoral systems and none seem perfect. Nonetheless, at least we now know what we're looking for in a system.
This question of optimizing the decision-making process was studied by an exceptional American economist and Nobel laureate named Kenneth Arrow. Arrow came up with a fundamental result - the "Impossibility Theorem". Through this thesis, Arrow puts forward the 5 conditions that are necessary for an optimal system.
The 1st is Nondictatorship : we should always consider the preferences of every individual before making a decision.
The 2nd is Individual Sovereignty : each individual should be able to order the choices in any way he desires.
The 3rd is Unanimity : if every individual prefers one choice to another, then the group ranking should do the same.
The 4th is Freedom from Irrelevant Alternatives : if a candidate is removed, then the overall order should not change.
The 5th is Uniqueness of Group Rank : the system should yield the same result whenever applied to the same set of candidates.
What does this really mean? Well, In essence, the Impossibility Theorem says that there is no electoral system that can possibly satisfy these conditions. There you go: the perfect political decision-making system does not exist. Now, I understand that you may find this surprising or even disheartening. Nevertheless, we must not let the absence of perfection in the realm of political decision-making hinder our pursuit of a simply better way to make decisions. Sometimes we have to accept that perfection just isn’t achievable. Instead, let us embrace democracy’s imperfections with open arms, and let our imaginations run wild with ideas to improve the way our society operates. Because, as Winston Churchill once said: “Democracy is the worst form of government, except for every other form that has been tried.”
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