We consider a decision problem where a group of individuals evaluates multi-attribute alternatives. We explore the minimal required agreements that are sufficient to specify the group utility function. A surprising result is that, under some conditions, a bilateral agreement among pairs of individuals on a single attribute is sufficient to derive the multi-attribute group utility. The bilateral agreement between a pair of individuals could be on the weight of an attribute, on an attribute evaluation function, or on willingness to pay. We investigate cases in which each individual's utility function is either additive or multiplicative. In the additive case, the group utility can be represented as the weighted sum of group attribute weights and group attribute evaluation functions. In the multiplicative case, the group utility takes a more complex form.

While recent deep learning methods have made significant progress on the video prediction problem, most methods predict the immediate or a fixed number of future frames. To obtain longer-term frame predictions, existing techniques usually process the predicted frames iteratively, resulting in blurry or inconsistent predictions. In this thesis, we present a new approach that can predict an arbitrary number of future video frames with a single forward pass through the network. Instead of directly predicting a fixed number of future optical flows or frames, we learn temporal motion encodings, i.e., temporal motion basis vectors and a network to predict the coefficients. The learned motion basis can be easily extended to arbitrary length at inference time, enabling us to predict an arbitrary number of future frames. Experiments on benchmark datasets indicate that our approach performs favorably against state-of-the-art techniques even for the next frame prediction setting. When evaluated under 5-frame or 10-frame prediction settings, the proposed method obtains bigger performance gains over the existing state-of-the-art techniques that iteratively process the predictions.

For decisions whose consequences accrue over time, several techniques are possible to compute total utility. One is to discount utilities of future consequences at some appropriate rate. The second is to discount per-period certainty equivalents. And the third is to compute net present value of various possible streams and then apply utility function to these net present values. When consequences are income streams, our main result shows that for a strict concave utility function, discounting utilities of incomes or discounting per period certainty equivalents can result in a paradoxical preference for receiving more money later to more money now. For income streams, the correct approach is to …rst compute net present values of various possible income streams and then take the utility of such net present value. The discounted utility model is appropriate for consumption streams, provided that the time intervals between periods are sufficiently large. Otherwise, we have the unrealistic situation where a short delay in consumption produces a discontinuous jump in the utility evaluation.