Kidney Exchange Programs (KEPs) facilitate the exchange of kidneys, and larger pools of recipient-donor pairs tend to yield proportionally more transplants, leading to the proposal of international KEPs (IKEPs). However, as studied by Mincu et al. [2021], practical limitations must be considered in IKEPs to ensure that countries remain willing to participate. Thus, we study IKEPs with country-specific parameters, represented by a tuple Γ, restricting the selected transplants to be feasible for the countries to conduct, e.g., imposing an upper limit on the number of consecutive exchanges within a country's borders. We provide a complete complexity dichotomy for the problem of finding a feasible (according to the constraints given by Γ) cycle packing with the maximum number of transplants, for every possible Γ. We also study the potential for countries to misreport their parameters to increase their allocation. As manipulation can harm the total number of transplants, we propose a novel individually rational and incentive compatible mechanism Morder. We first give a theoretical approximation ratio for Morder in terms of the number of transplants, and show that the approximation ratio of Morder is asymptotically optimal. We then use simulations which suggest that, in practice, the performance of Morder is significantly better than this worst-case ratio.

We introduce new power indices to measure the a priori voting power of voters in liquid democracy elections where an underlying network restricts delegations. We argue that our power indices are natural extensions of the standard Penrose-Banzhaf index in simple voting games. We show that computing the criticality of a voter is #P-hard even in weighted games with weights polynomially-bounded in the size of the instance. However, for specific settings, such as when the underlying network is a bipartite or complete graph, recursive formulas can compute these indices for weighted voting games in pseudo-polynomial time. We highlight their theoretical properties and provide numerical results to illustrate how restricting the possible delegations can alter voters' voting power.

In rank aggregation, members of a population rank issues to decide which are collectively preferred. We focus instead on identifying divisive issues that express disagreements among the preferences of individuals. We analyse the properties of our divisiveness measures and their relation to existing notions of polarisation. We also study their robustness under incomplete preferences and algorithms for control and manipulation of divisiveness. Our results advance our understanding of how to quantify disagreements in collective decision-making.

Iterative voting allows a group of agents to take a collective decision in a dynamic fashion: a series of plurality elections are staged, making the relative scores of the candidates public after each round. Voters can thus adjust their ballots at each step until the process converges (or a maximal number of steps is reached). Research in computational social choice has shown that this method has the potential of reaching good-quality decisions while at the same time being easy to explain to voters. This paper presents our implementation of iterative voting on a voting platform accessible on the web.

Liquid democracy bridges the gap between direct and representative democracy by allowing agents to vote directly on an issue or delegate to a trusted voter. Yet, when applied to votes on multiple interconnected issues, liquid democracy can lead agents to submit inconsistent votes. Two approaches are possible to maintain consistency: either modify the voters' ballots by ignoring problematic delegations, or resolve all delegations and make changes to the final votes of the agents. We show that rules based on minimising such changes are NP-complete. We propose instead to elicit and apply the agents' priorities over the delegated issues, designing and analysing two algorithms that find consistent votes from the agents' delegations in polynomial time.

We propose a generalisation of liquid democracy in which a voter can either vote directly on the issues at stake, delegate her vote to another voter, or express complex delegations to a set of trusted voters. By requiring a ranking of desirable delegations and a backup vote from each voter, we are able to put forward and compare four algorithms to solve delegation cycles and obtain a final collective decision.