plurality voting has a fundamental flaw it works well in a two-way race but as soon as you have more than two options on the ballot weird things can happen introducing additional choices can tilt things in favor of another candidate here adding a yellow Party candidate to the ballot helps the orange party this violates the independence of irrelevant Alternatives rule adding a yellow Party candidate should only be beneficial to the yellow Party candidate and not harmful to any other candidate are five rules for a voting system lay out the properties we would like to have in the way our individual preferences are aggregated into society's preferences let's look at some other voting systems when we talked about agenda setting we found that if there's no condorsay winner the person who sets the agenda decides which policy will be enacted this violates a rule about non-dictatorship here the preferences of one person are all that matters in the end many people support switching our voting system to instant runoff voting and some places already have with instant runoff voting each voter ranks their choices options with the least support are eliminated and votes are reallocated to next best choices until an option gets over 50 percent of the votes this flowchart shows how to tally the votes voters will have indicated their first second third fourth fifth choices and so on there can be as many options you want and voters can rank as many of them as they would like first we've count the voters first choices if a candidate has over 50 percent of first place votes they win if not then we eliminate the last place candidate anyone who ranked the eliminate eliminated candidate as number one now has their votes instantly recast in favor of their second choice their votes now count as votes for their second choice and we count again candidates are eliminated and votes recast until one candidate has over 50 percent of the vote we can see this in action with our previous set of Voters the orange Party candidate will be a and the red Party candidate will be B and the yellow Party candidate is C written on each voter is how they would rank the candidates if we tally up the top choices of each voter we get six votes for a four votes for B and three votes for C no candidate has a majority yet since the yellow Party candidate got the fewest votes though they are eliminated now the voters who rank C first have their ballots redistributed to their second choice which for all three is B candidate a gets six votes while candidate b gets seven votes and is declared the winner certainly this system of voting satisfies all of our voting criteria right to see why it doesn't I'm going to pick on this voter now in purple right now their preferences are B then C then a and in the end B wins but what if I change their preferences what if they decide they like C more than b with their new preferences of C then B then a we can retali the votes a gets six first place votes b gets three votes and C gets four votes now it's B that has the fewest votes and gets eliminated the three red voters are reallocated to their second choice two of them list a as their second choice so a gains two votes while one reallocated voter lists c as their second choice so C gains one vote and a is declared the winner are purple voters switched their preferences between B and C and suddenly A1 this violates citizen sovereignty when ranking C first instead of B we want our voting system to either return c as the new winner or keep b as the winner think about how the purple voter must feel they still think B is better than a but by changing their Preference they handed the election to A and B got eliminated we don't want our voting system to require us to be strategic about our voting choices we want to be able to just put down what we really think but this system encourages people to lie about their true preferences in order to achieve an outcome closer to their true desire in his doctoral dissertation The Economist Kenneth Arrow proved that a voting system which satisfies all of our criteria simply does not exist there's no way to aggregate the ranked preferences of each individual into a preference for society without violating one or more of these rules arrows and possibility there is my favorite Discovery in all of Economics not only am I Blown Away by the fact that Arrow was able to prove this but it's also just the first of a large number of incredible contributions Arrow made to the field of Economics over his career I think it also helps explain why democracy is so hard it helps explain why Winston Churchill said many forms of government have been tried and will be tried in this world of sin and woe no one pretends that democracy is perfect or all wise indeed it has been said that democracy is the worst form of government except for all those other forms that have been tried from time to time but there's one more thing that makes arrows impossibility theorem so special markets are the one thing which can satisfy our criteria markets ask us to translate our preferences into a willingness to pay they take our ordinal preferences which are our rankings and turn them into Cardinal preferences which are our choices with relative value arrows and possibility theorem only applies to ordinal preferences and so markets spare us the many challenges we find in government from infiltrating our daily economic lives so let me leave you with this economics is for understanding the world it gives us tools for insight into how things really work and helps us to see the world as it really is in our class we've explored the beauty and wonder of the price system while identifying how human nature gets in the way of its proper functioning I hope that with these new insights you will be better equipped to navigate the choppy Seas of Life towards your hopes and dreams