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Welfare
I like to describe the aggregation of preference issues in terms of manipulation.
Majority voting is bad because the outcome can depend on the order in which
the vote is taken and this can lead to agenda manipulation. Rank-order voting
is bad because introducing a new alternative can change the outcome of the
process, which creates another way to manipulate the political process. Arrow’s
theorem can be interpreted to say that there is no way to avoid such manipulation
possibilities.
However, that being said, we typically resort to looking at simple ways
to aggregate preferences through the use of welfare functions. The essential
point to get across here is the connection between Pareto efficiency and welfare
maximization: every welfare maximum is efficient. Furthermore, subject to the
usual convexity conditions, every efficient allocation is a welfare maximum for
some welfare function.
The fair allocation stuff is fun. Students like it, since it addresses problems
of equity in a nice way. I sometimes talk about other methods of fair division,
such as one person cuts and the other chooses, etc.
Welfare
A. Incorporate distributional considerations into the analysis
B. Need some way to compare individual preferences or utilities
C. Aggregation of preferences
1. majority voting
D. Arrow’s impossibility theorem
E. Social welfare fuctions
1. add together utilities in some way
84 Chapter Highlights
F. Maximizing welfare
1. every welfare maximum is Pareto efficient. Figure 30.1.
G. Fair allocations
1. generalized the idea of symmetric treatment
2. if ui(xj)>u
i(xi), then we say that ienvies j
3. typically will be possible to find allocations that are envy-free and efficient
84 Chapter Highlights
F. Maximizing welfare
1. every welfare maximum is Pareto efficient. Figure 30.1.
G. Fair allocations
1. generalized the idea of symmetric treatment
2. if ui(xj)>u
i(xi), then we say that ienvies j
3. typically will be possible to find allocations that are envy-free and efficient
