Making Better Group Decisions Voting, Judgement Aggregation and Fair Division w


Hello, my name is Eric Pacuit, and I’m a Philosophy
professor here at the University of Maryland at College Park, and I would like to invite
you all to take my course, Making Better Group Decisions: Voting Theory, Judgement Aggregation
and Fair Division. This is gonna be a really interesting course in which we look at the
problems that arise when a group of people come together to make a group decision. The
course is gonna be divided into three parts, corresponding to the different types of group
decision problems you might face. The first part is going to look at problems of voting,
and these are problems in which you have a set of candidates or a group of objects, and
everybody has different opinions, different preferences about these objects and you need
to come together and make a group decision, select one of those objects. So, for example,
suppose that you’re going out to dinner with a group of friends, and you need to decide
which restaurant to go to. If everybody agrees on one particular restaurant, then the decision’s
easy, you simply go to that restaurant. But how do you make the decision if people have
different opinions, different preferences over the different restaurants? Some people
like the French restaurant the best, some like the Italian restaurant the best, and
others think the Indian restaurant is the best. How do you make a decision in that case?
Of course, you can’t come to a decision that will make everyone happy since everybody has
differing opinions, but perhaps there is a choice you can make that will make the people
as happy as possible. The second type of problem we’re going to face is, we’re going to think
about is the problem of judgement aggregation, and this is similar to voting problems, except
with one important difference. With problems of judgement aggregation, there’s typically
a fact of the matter, something, some fact that we want to uncover as a group. So the
typical example there is you have a jury, and you need to decide the guilt or innocence
of a particular defendant. So everybody forms an opinion and they need to, we need to somehow
combine or aggregate those opinions to form the overall group judgement. And in these
settings, we’re not always interested in being fair and fairly representing everybody’s opinions.
What we’re really interested in is whether or not the group decision is correct, whether
or not it latches onto the truth. And finally, we’re gonna look at problems of fair division,
and these are problems in which you have some set of objects, and you need to fairly divide
these objects among everybody in the group. So for example, imagine that you’re at a child’s
birthday party, and there’s a cake, and we want to fairly divide this cake up among all
the hungry children at the party. Now if the cake is completely uniform, for example, all
vanilla, vanilla cake with vanilla icing, then it’s easy. You just ensure that everybody
gets the exact same size piece. But what do you do if some of the cake has chocolate icing
and other has vanilla icing and part of it has strawberry icing, and the children each
have different preferences, so some really like chocolate, some really like vanilla.
How do you divide the cake up fairly in that case? And what do you do, this will be familiar
to anybody who’s recently been to a child’s birthday party, what do you do when there’s
that one toy that’s on the cake that all the children really, really want? How do you divide
the cake up fairly in those cases? And what does it even mean to say that the division,
the way you distributed the cake is, in fact, fair? Surely, all the children should feel
that they received their fair portion, so if there’s five children, each child should
feel as if they got one fifth of the cake. But perhaps we would want to impose another
condition, envy freeness, so that no child is envious of another child’s piece. So as
you can see, these are all very practical problems and we’re going to think about these,
the different methods and puzzles that arise when a group of people come together to make
a decision. Now, I just want to conclude by mentioning a few things about the mathematical
component of this course. The way I’m going to think about these problems is through the
lens of mathematics, so I’ll be shedding, looking at these problems from a slightly
different perspective than what a lot of you are used to, and certainly, for those of you
who like logical puzzles and simple mathematical puzzles, this course will be right up your
alley. But I also want to encourage those of you who don’t have a strong background
in mathematics or perhaps don’t even consider themselves that strong in mathematics, I would
like to encourage you to take this course as well because in, I’m not going to have
any prerequisites. There’s no, you don’t need any particular background in mathematics,
so you will be exposed to basic mathematical thinking while focusing on very concrete and
practical problems. So I really look forward to creating these lectures, and I look forward
to seeing you all in the discussion boards.

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