Condorcet Voting Paradox

Alright, now let's discuss another issue related to voting. The Condorcet voting paradox. Alright, Condorcet voting paradox. This is that the majority voting can result in inconsistent results. Okay. We might get inconsistent results when we do a majority vote, right? The majority vote is the majority wins whenever whoever is in the majority wins the vote. So let's think of this situation where we've got three groups faced with three choices. So the first group has these preferences, right? First choice, second choice, third choice. They pick A over B. Over C. Right? Second group B. C. A. Third group C. A. B. So let's see what happens if we send these things to a vote and they have to go up against each other. Right? The first one would be if we sent A versus B to a vote. Right? So let's go here and see who would vote for what? In A. Versus B. So the first group, would they pick A. Or B. If that was the vote? Well, their first choice is A right. The first groups, first choice is A. So they would pick A. What about the second group? The second group's first choice is B. So they would pick B. And how about the third group? The third group's first choices C. But that's not available, right? This is a. Vote between A. And B. So they're gonna vote for A. And A. Is gonna win this vote A wins the vote between A and B. Now, what happens if we put the vote between B and C. Between B&C. Well, what is group one gonna vote for? They can't get their first choice of a. So they'll take their second choice of B. What about group to? Well they get their first choice right? They're gonna vote for B. And group three. Their first choices C. Which is uh it is it is in the vote. So that is what they're gonna vote for. Group three votes for C. In this case be wins right? B. Comes out oversee. And guess what's gonna happen in this third scenario? If you can't guess, let's go ahead and pull it out. So we've got C. Versus A. In this case, what is? Group one gonna pick? Group one is gonna pick their first choice of A. And they'll vote for a group to, well their first choice of B is not available. So they're gonna vote for C. And three is gonna vote for their first choice of C. Up here. Right? So group three is gonna vote for C. And we're gonna see that C. Wins. Right? So C. Wins. And what we see is that when there are more than two options, what's gonna happen is that the order of the voting agenda influences the outcomes? Okay, so this condorcet voting paradox showed us that depending on the pairing A one B one C. One but if a BB and B beats C. But then see beat A right this transitive property, right? Remember we studied algebra and we had something like if A equals B and B equals C. Well then A must equal C. Right? That's something that we learned in algebra. Well, that's totally falling apart right here, right? Because A was able to beat B and B was able to beat C. So we would imagine that they could beat C. But then see beat A. Right. Crazy. So this is the paradox here. Alright, So I guess let's pause here and then in the next video, let's see how we can use this knowledge of the agenda and the order of the vote to force certain policies to win. Okay, let's let's pause here and then we'll continue with that example.

Alright, So now let's see how the order of the voting agenda is going to affect the outcomes of the vote. Okay? So if we're policyholders or were the policy makers, we might have certain agendas, right? Maybe we want a to win personally. We want to win. So we can manipulate the order of the vote to force A to come out on top. So let's see what happens here if we want a to win. Well, the first thing we're gonna want to do is we're gonna want to get rid of C. Right? Because if we look above sea beats a right C versus A. C. Won the vote. So the first thing we wanna do is we wanna vote between B versus C. Right? And as we saw above when B went against C, we'll be was the the agenda that came out on top. Right? So be wins in that case. So now that B one C. Is off the table, C. Is no longer being voted for Cosby was preferred. So now we set a vote of A versus B. Right? And now if we go A vs. B, look what happens up above, we already figured this out. And we saw that A wins, Right? So A wins and that knocks out B. And A becomes the policy that gets instated, right? A wins the overall vote and becomes the policy. All right, let me get out of the way here. And let's let's see what we would do if we want C to win. All right, Let's see what we want to do if C wins. So notice if we go B versus C up here, if we're doing the B versus C, B is gonna beat C. So we need to get rid of be first. So, the first vote we want to do is A versus B. If we do A versus B, well, who's gonna win? An A vs. B. A. Wins. Right. So B is off the table, B is no longer being voted on, and now we can do the vote of A versus C. Or as we have it written above sea versus A. And what's the outcome there? Is that C wins? Okay, So we can use this knowledge or at least politicians can use this knowledge to their advantage when they're setting the voting agenda to get their policies to be the ones that go through. Alright, so, another conclusion we see here is that majority voting by itself does not necessarily provide the outcomes that society wants, right? It's not just gonna create the right outcomes. Um The majority voting can be manipulated, and just as we saw above. All right, So, let's go ahead and pause here and move on to the next video