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# System prepended metadata

title: Meeting Notes 10/6/20

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# Meeting Notes 10/6/20

Discussed last time:
* investment incentives in VCG vs. information acquisition
* related literature on committee design with endogenous information
* pivotality is $O(e^{-n})$ unless vote is "close"

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Question: can we rely on pivotality to provide truth-telling incentives or not?

Consider binary voting with $\gamma$-robustness, i.e. agents can act suboptimally by additive constant $\gamma$. (This is a way to capture the strength of the agent's incentives under a given mechanism.)

My guess is that VCG with optimal sample size is $\epsilon$-efficient where
$$
\epsilon=\Theta\left(\frac{1}{\sqrt{\ln(1/\gamma)}}\right)
$$
assuming we define efficiency w.r.t. worst-case distribution.

Implications for information acquisition:
* If $\gamma=0$ and there is some (exogenous) probability $p$ that the agent is informed (i.e. no costs of acquiring information) then the mechanism we've been discussing should still work, with budget that depends on $p$.
* The mechanism would remain sensitive to agent's that make small mistakes or agents that incur an additional cost of writing down or determining their value after having collected information.

Suppose we know the distribution of outcomes of informed voting, without knowing the information itself. We can optimize the sample size in expectation over that distribution of informed outcomes.


Binary vote. Don't know in advance the issue, but know that each individual has positive or negative opinion. Independent with probability $p$. Pay cost $c$ to learn your own opinion. +1 if your preference passes, -1 otherwise. Vote randomly if you don't learn your opinion.

If there were dictator (sample size 1) then an individual will pay cost.

Taking $n=1$ is better than $n=\infty$.

What is the right number of samples? Maybe we know $p$ but not the "sign".

Multiple equilibria?