This talk focuses on the quantification of power in voting systems where the exercise of voting rights is delegable and delegations are transitive. Building on the Banzhaf-Penrose power index for weighted voting games, I will present an index that can quantify the influence of both voters and delegators, and characterise it axiomatically. Then, using this index, I will study games where agents are engaging in a truth-tracking task but their utilities depend on competing interests: on the one hand they want to improve their decision-making accuracy (by delegating to more competent agents), and on the other hand they want to retain power in the system. In such games power-seeking behavior, in equilibrium, appears to have a balancing effect on the number of delegations that agents are able to accrue, thereby mitigating possible power imbalances in the system.

Liquid Democracy is a voting system touted as the golden medium between representative and direct democracy: decisions are taken by referendum, but voters can delegate their votes as they wish. The outcome can be superior to simple majority voting, but even when experts are correctly identified, delegation must be used sparely. We ran two very different experiments: one follows a tightly controlled lab design; the second is a perceptual task run online where the precision of information is ambiguous. In both experiments, delegation rates are high, and Liquid Democracy underperforms both universal voting and the simpler option of allowing abstention.

We propose a new mechanism to elicit voters' cardinal utility functions over a set of policy alternatives, and select (with high probability) the alternative that maximizes a weighted utilitarian social welfare function. Each voter reports a "valuation", which assigns a numerical value to each alternative. Like Quadratic Voting, our mechanism incentives truthful reports by imposing on each voter a cost, which is a quadratic function of her valuation. But instead of money, this cost is paid out of a budget of "voting points" which the voter can use to vote in many different decisions. We show that, in equilibrium, each voter's valuation is a positive affine transformations of her true vNM utility function.

One of the challenges of committee voting is to aggregate information when committee members have different quality of information. In this case, more complex rules allow voters to better aggregate information by endogenously allocating more decision power to members with better information.

We consider two polar examples of voting rules in terms of complexity: majority voting MV and continuous voting (CV). Under MV, members can vote "yes", "no", or abstain. Due to its coarseness, MV does not allow voters to properly express the quality of their information: it either ignores information of the poorly informed or it attaches the same weight to votes form highly informed. Under CV, instead, voters have incentives to choose the optimal weights that implement the efficient decision for any information structure. But the desirable properties of CV might be overturned by the cognitive costs to deal with the additional complexity.

We compare MV and CV using laboratory experiments, and we also study participants' preferences over these. We find that CV, despite the higher cognitive costs, does better than MV on average, but the difference is lower than theoretically predicted. One of the significant departures from theory is that voters with intermediate information quality attach too much weight on their votes. Communication makes these differences over mechanisms disappear. Finally, despite the higher average welfare under CV, both rules get similar support.