In France we are lucky to live in a democracy, and the vast majority of us think that we have the best political system. One thing that comes along with being a democracy is the power of the people to choose the politicians that govern them. That’s good but the way we choose them, are we sure it’s the best? No, not really. Actually it’s pretty bad and we can do much better Let’s reform the presidential election!! In France, under the 5th Republic, the big election is the Presidential Election The French President is elected in a two-round uninominal election. Uninominal means that we vote for only one person. During the 1st round we have plenty of candidates….. …and we keep the best two for the 2nd round. Seems like a very simple system, to the point that we can’t see how it could be better. And yet we know that this system has several flaws. The best example is the 2002 French Presidential Election A little reminder for those who can’t remember (or are not French ^^) On April 21 2002, after the 1st round…. ….Jacques Chirac, the President at that time, came in first with 19,9% of the votes. And to everybody’s surprise, Jean-Marie Le Pen (extreme right) comes in second with 16,9% of the votes. Lionel Jospin came in third with 16,2% of the votes. For the 2nd round, Chirac is easily reelected with 82% of the votes. What is weird in that election is that Lionel Jospin is eliminated after the 1st round by a small margin….. …..but all the polls predicted he very well could have won against both Le Pen or Chirac if he had been part of the 2nd round. Back in 2002 we had attributed his lost to the presence of other “little” candidates on the left. Jean-Pierre Chevènement got 5,3% Christine Taubira got 2,3% We had already seen something similar in the preceding election in 1995. Edouard Balladur, the extreme favorite just a couple weeks before the election…. …..lost by very little during the 1st round And we think that if Philippe De Villiers who collected 4,8% of the votes had not run….. ….Balladur would probably have been the candidate from the right for the 2nd round instead of Chirac. The problem with these elections is not what we actually thought of the candidates….. …but the fact that every time we have a candidate with a real chance of winning the election…. ….but that candidate doesn’t make it to the final round because of some “little” candidates with similar stances…. ….stealing the votes from him even though they don’t have a real chance of getting elected. That is a weird situation Let’s make an analogy with sports Imagine at the final of the 100m at the Olympics the 3 slowest runners can hold back the 3 fastest by their shorts So that the one who wins the race wasn’t actually the fastest but the runner who managed to be held back the least. We would find that completely stupid, illogical and against all fair play and sportsmanship. And yet that’s exactly what happens at the presidential election. The outcome is decisively influenced by the presence or absence of certain smaller candidates. And yet we find that fair… but we’re talking about something far more important than the outcome of a 100m dash! It’s just the future of the country!!! But who cares! We’ve all gotten used to living with this bizarre rule to such a point that we find it almost normal. To compensate, we invented the “useful vote” The principle behind this vote is to force ourselves not to vote for the person we most prefer, the one we would most liked to be elected…. …..but instead vote for one that we like less but who has a greater chance of winning. And then there’s the opposite, the “Protest vote”, where we vote for someone that, deep down, we don’t really want to see elected. Ok so fine, we have a democracy, and we get to choose our leaders, but the system is completely messed up. It’s a little bit of a shame isn’t it? Can’t we find a different method to elect the president that would avoid all these problems? A way to vote that would be more just, more thorough and more representative of the people. Well guess what? That question has been studied by political scientists and mathematicians…. ….and now we can look at it through the eye of science. As we saw it, what’s wrong with our current system is that the score of little candidates who have no chance of winning…… ….can affect who has the chance to participate in the 2nd round of elections, and thus the potential winners. Small side note : this situation is not unique to France. In the USA it’s even worse as there is only 1 round of national voting. The tradition in the USA is that there will only be 2 major parties and candidates…. …but as soon as a 3rd party presents itself it becomes a big mess. In 1992, George Bush Sr, went up against Bill Clinton…. …. and normally Bush would have won. But there was a 3rd candidate, Ross Perrot, an independent (green), who was right leaning….. ….who received almost 20% of the votes…. …and so certainly took some of Bush’s votes. And Bill Clinton won. To avoid this kind of situation, in France or the USA…. ….one solution is to have more rounds of voting. In the most extreme of this scenario…. …. we could imagine eliminating only one candidate at each round of voting… …and have as many rounds as we need to elect the winner. If we really did it like that… …everyone would be free to vote for the little candidate of their choice during the first rounds…. ….without that affecting the next rounds. But now you’re gonna tell me that this sounds a little bit complicated…. …during the last French election we had 10 candidates….. …so should we have done 9 rounds of voting? It would have taken us several months to elect the President. Actually we don’t! 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. So here is how we do it…. To simulate the 1st round of voting, we only look at who was ranked 1 on each ballot….. …we calculate the % of each candidate and we see who got last…. ….then we eliminate that name from each ballot. To simulate the 2nd round, we again take the 1st choice on each ballot….. …..except for those who ranked the candidate that we got rid of before as their 1st choice. For them, we take the 2nd choice of their list. We once again calculate the % of each candidate and get rid of the last one. We repeat that process until we have a winner. This voting process truely exist…. …it’s called “Alternative Voting” It is used for example to elect the House of Representatives in Australia… …to elect the Irish President and in some American municipalities. The superiority of this method lies in the fact that we can better express our true opinions The problem with the uninominal voting system is that we say absolutely nothing about what we think of the other candidates…. That means that we reduce all of the complex opinions that we have about the candidates for the choice of only one name….. ….whereas with the “Alternative Vote” we can truly express our opinion in a deeper way because we rank all of the candidates. so is the “Alternative vote” the perfect way of voting?? ehhh. Actually it turns out not really. First off, for the voters it is not very simple…. …usually we know which candidates we like and which one we hate…. ….but being able to rank all the candidates when there are 10 or 12 isn’t easy. This method allows us to rank lot’s of little candidates like we find in France…. …but as soon as we get to the second-to-last round, where there are only 3 candidates left…. ……we find ourselves back in the regular (French) situation of a 2 round election. And now we’ll see that with just 3 candidates and 2 rounds left some weird things can happen. So let’s imagine there are only 2 rounds left…. ….whether we got there the traditional way or the “Alternative” way, it doesn’t matter…. Let’s say we have 3 candidates… François…..Nicolas….and Marine. I’m purposely choosing real life politicians (French) so it’s easier for you to imagine…. ….but what I’m about to demonstrate applies in a very general way…. …. it’s related to the mathematics of the vote and not to the candidates or their parties. So let’s say 34% ranked François before Nicolas, and Nicolas before Marine. Then 32% ranked Nicolas before François, and François before Marine. And 34% ranked Marine before Nicolas, and Nicolas before François. It’s a very simplified situation but also relatively plausible right? Let’s simulate the 1st round. Everyone votes for their preferred candidates. François has 34%, Marine 34% as well but Nicolas only 32%….. so Nicolas’ out. Now the 2nd round… ….those who voted for Nicolas for the 1st round now find themselves with François. ….so François gets 66% and Marine 34%. So François wins by a landslide. So now imagine that things didn’t exactly happen like that….. ….imagine that François had a more effective campain… ….and that he was able to take 3% of Marine’s votes. Then we would have the following percentages for the rankings. François>Nicolas>Marine : 37% Nicolas>François>Marine : still 32 % And Marine>Nicolas>François : 31% Now we simulate the 1st round again… François 37%, Nicolas 32% and Marine 31% So Marine is eliminated at the 1st round. If we simulate the 2nd round, this time we end up with Nicolas winning with 63% of the votes. See the paradox? In the 1st situation, François is elected…. ….but if he gets more of the 1st round votes, he could end up losing!!! This is called “Arrow’s Paradox” Whether or not it’s a classic or alternative system…. …. as you progress in the rankings… ….. your chance of winning could decline…. ….which is absurd!! Besides the fact that’s it’s completely incoherent…. …..it breeds the ” strategic vote”. This is when, one candidate’s supporters, François…. ….should find it in their best interest to actually not to vote for him in the 1st round…. ….but to vote for Marine to make it easier for him in the 2nd round. The ” strategic vote” is when we don’t vote for the person we want to see win…. …. but rather to exploit the defect of the system to help our candidate. Here is another paradox of the classic system…. Imagine 3 candidates : Ségolène, Nicolas and François. I continue with real life politicians (French) but please note that it’s a different François. Imagine people rank them in the following ways 40% of the voters prefer Nicolas to François, and François to Ségolène. To make it simple you can call those voters the right wing… 40% of the voters prefer Ségolène to François, and François to Nicolas. Let’s call them the left wing 10% of the voters prefer François to Nicolas, and Nicolas to Ségolène. Let’s call them the Middle-right 10% of the voters prefer François to Ségolène, and Ségolène to Nicolas. Let’s call them Middle-left Let’s simulate the 1st round…. ….we take the 1st choice of each voters… ….Nicolas and Ségolène both get 40%… ….François gets only 20% and finds himself eliminated. The 2nd round is between Nicolas and Ségolène. And yet if we did a duel between François and Nicolas only… ….François would win 60-40. …and if we did a duel François-Ségolène, he would also win…. So François is capable of beating each opponent individually but is unable to access the final round. Once again, if we compare it with sports competitions, it’s weird. This example is not completely fictional… …. in the 2007 French election there were 12 candidates and the polls predicted that François Bayrou would beat any other candidates in a duel….. ….except he didn’t make it to the 2nd round. This is not something new… ….It was actually noticed by Condorcet in 1785…. …..a French mathematician and philosopher who first studied different voting processes in a scientific manner. And based on his findings…. … Condorcet came up with his own voting process…. called the Condorcet Method. We organize Electoral duels between each candidate…. …. and we keep the one who can beat everyone else. Seems like a good plan? Except Condorcet noticed certain situations where it didn’t work. There are certain situations where no candidate is able to beat all of the others. And that creates a very odd situation. Let’s say we have 3 candidates named A B and C…. Let’s say 1/3 prefers A to B and B to C. 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 do a duel A against B, that means we leave out C. A beats B If we do a duel B against C, B wins. In a duel A against C, C wins. That means that no candidate can win all of his duels. That is weird… …. we call it Condorcet’s Paradox. Now imagine that A was elected, it doesn’t matter by which method… If you organize a referendum on the day after the election…. ….2/3 of the population would choose to replace him by C…. ….because C beats A in people’s opinion. But if you do that, 2/3 of the population would choose to replace C by B right away…. …because B beats C in people’s opinion. …Except that if B is president, 2/3 of the population would agree to go back to A as president. So we need to find something else! 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… … for example 1 point for the last one, 2 points for the second to last…. …and N points to the 1st if we have N candidates. And the winner is the one with the most points. If we apply this to the example with Nicolas, François and Ségolène…. ….. we end up with 190pts for Nicolas and Ségolène…. …and 220pts for François, who would win the election. This method is actually used in some sport competitions…. …. and for some elections at the French Academy of Science. So it seems perfect? Humm not really, first of all, it depends how you decide to deals the points…. … and just like in a classic election… ….small candidates can have an influence on the big candidates… …. so no it’s not that ideal. So this is a bit discouraging… ….. we looked at a couple of electoral systems and none seems perfect. But at least now we know what we’re looking for. We need a system that satisfy at least 2 conditions… …. the 1st is that when you progress in the polls, you progress in the final ranking… …. we saw that with a classic voting system, that is not always the case. The 2nd condition is that when you add or remove a candidate with little chance…. ….it doesn’t affect the outcome for the leading candidates, like in a 100m dash. This question was studied by an American economist named Kenneth Arrow. Arrow came up with a result called the “Impossibility Theorem” Basically it says that there is no electoral system that can satisfy both conditions. There you go, “Game Over”, the perfect system doesn’t exist…. … it’s a little bit depressing… ….the “Impossibility Theorem” tells us that no matter what we do, we can’t properly elect the people running our country. Except Arrow’s theorem is only valid for voting systems where people are ranked in order… … and you can get around that problem by not ranking the candidates but judging them individually… …and we can easily do that using an electoral system called the “Approval vote” In that system you can vote for as many candidates as you want….. …you can’t vote twice for the same candidates…. …but you choose to give a vote to all the candidate you like. In the end you end up with the approval rate of each candidate. This election process is not affected by minor candidacy… …If you like multiple candidates, you can vote for all of them… A big advantage to that system is that it is very easy to put in place…. ….you just need to tell people that they can vote for multiple candidates. One round and that’s it…. …the problem is that you can’t grade the candidates… ….there is no difference between your favorite and the others… ….to go further it would be great if we could grade each candidate on a scale….. ….this is already being done when we want to rank students, movies or gymnasts… …..so why not political figures? We could imagine a system where we grade each candidate on a scale from 0 to 10….. … we would need to find a common scale…. ….7/10 for me, might not mean the same for you. Another problem is that you could weight in more for your favorite candidate… For example you give 10/10 to your favorite…. …and 0/10 for all the others. Even though it might not be the way you feel deep down. In the end, having a president elected with grades might not be the best solution. To avoid these problems, 2 French scientists : Rida Laraki and Michel Balinski… …came up with a voting system that overcame all the problems that we talked about since the beginning… ….it is called the “Majority Judgement” method. This method is extremely easy to put into place…. …instead of giving grades (numbers) to the candidates… …we give them ranks from “excellent” to “Absolute Crap”. Excellent, Very Good, Good, Good Enough, OK, Bad and Absolute Crap. This is what the ballot would look like. “To be the French President, having taken all the elements into consideration…. …I hereby judge the candidates to be : ” For each candidate you check the corresponding box. How do you end up with the results? For each candidate, each rank represent a different %. Let’s take an example…. Imagine a candidate to which 9% of the voters….. …attributed “Excellent”.. …very good 14%.. …good 16% …..Good Enough 15% ….OK 18% …..Bad 15%…. ….Absolute Crap 13% Graphically it looks like this. How do we read these results? 9% of the voters rated him as “Excellent”… …23% would rate him at least “Very Good”…. …that means both “Very Good” or “Excellent” together. 39% would rate him at least “Good” 54% would rate him at least “Good Enough” “Good Enough” is then the majority judgment of that candidate…. …so more than half of the voters judged him at least to be “Good Enough”. Finding the Majority Judgment is very easy… …just draw a line at 50% and see where it falls. In this case ” Good Enough” To rank the candidates you just have to read each Majority Judgements rate…. ….the one approved by at least 50% of the voters… …the candidate with the best Majority Judgement wins the election. In case of a draw, you can sort them out with the actual rate. This is what we call the Majority Judgement method…. ….and we could easily use this method to elect Mr or Mrs President of our Republic. So what makes this method so great? First off, each candidate is judged individually… ….on his personal merit, independent of the other candidates. And so we don’t have the problem of little candidacies affecting the outcome of the election by presenting themselves….. …here if you add more candidacies it won’t affect the Majority Judgement of a given candidate. So there can’t be a “useful” vote, you just express your feelings about each candidate. Another advantage of this method is that Arrow’s Paradox doesn’t apply…. ….a candidate who progresses in the polls can’t have his final ranking going down. Moreover, with this method there is no incentive for a “strategic vote”…. …that means over rank your favorite candidate…. …if your favorite candidate received a Majority Judgement of “Good Enough”…. …if you voted “Excellent”, “Very Good”, “Good” or “Good Enough” it wouldn’t change anything…. …so you don’t have to exaggerate your vote… …you just have to vote sincerely with your personal opinion. Another advantage of this method : if all the candidates receive “Bad” or “Absolute Crap” Majority Judgements…. … the people can ask for new elections with all new candidates… …. and forbid the previous ones from running again. This method allows us to choose the people running our countries in a more precise and accurate way of what the people want. And perhaps reconcile the people with the politicians. If you also think we can use a better method to choose our Presidents….. …don’t hesitate to share this video…. ….especially to make more people aware of the method of the Majority Judgement. If you want to know more about it, I wrote an article on my blog… …or go watch this other video called “Statistics explained to my cat”… …which shows how with the same numbers you can end up with different results depending on the election method. As always if you like science you can subscribe to my channel…. …. and follow me on facebook or twitter…. …and financially support me on Tipee.com Thank you very much and see you soon.