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1st Semester 2020/21: Preference Extensions in Social Choice: Ranking Outcomes With Ties

Sirin Botan

This project will examine how we can reason about an agent's preferences over sets of objects, when we have only been given the agent's preferences over the objects themselves. These (sub)sets of the objects represent possible end results, one of which will be chosen in some way that is not known to the agent (meaning these end results are mutually exclusive). Often this topic comes up when we reason about strategic behaviour in multiagent systems. One prime example of this is agent preferences in voting when a voter has to compare two outcomes where there are ties between candidates.

To give an example--suppose I need to decide between two restaurants for dinner. The first restaurant only serves Italian cuisine, while the second serves Thai cuisine some days and and Japanese cuisine on others. I don't know ahead of time what the menu will be on the day I'll be at the restaurant. Suppose my food preferences are as follows: I prefer Japanese food over Italian food, and Italian food over Thai. Which restaurant should I prefer?

This problem has been adressed by economists and computer scientists (among others), and there are many proposed ways of extending preferences over objects to sets of objects---so-called preference extensions. For example, I may be an optimist who believes that my top choice from each set will be the end result. Or I may think of each set as a lottery, giving each element an equal chance of ending up as the final choice. These are two of many reasonable preference extensions.

The aim of this project is to give students an overview of such preference extensions and settings where they are employed. I will spend the first week giving lectures so we are all clear on the theoretic foundation. The second week students will choose a paper to read and present (I will give some options to choose from). The third and fourth week you will write a short paper. This can be a 'survey-style' paper that given an overview of a particular sub-topic, or a more 'research-style' paper where you identify (and then examine) a problem that is small enough so you can say something interesting about it in the two weeks you have.


Lectures, paper presentations, final paper.


Mathematical maturity. 


Assessment will be based on participation throughout the project and the final report. (pass/fail)

Ranking Sets of Objects by Prasanta K. Pattanaik, Salvador Barbera, and Walter Bossert