We investigate efficient ways for the incorporation of liquid democracy into election settings in which voters submit cumulative ballots, i.e., when each voter is assigned a virtual coin that she can then distribute as she wishes among the available election options. In particular, we are interested in fine-grained liquid democracy, meaning that voters are able to designate a partial coin to a set of election options and delegate the decision on how to further split this partial coin among those election options to another voter of her choice. The fact that we wish such delegations to be transitive -- combined with our aim at fully respecting such delegations -- means that inconsistencies and cycles can occur, thus we set to find computationally-efficient ways of resolving voter delegations. To this aim we develop a theory based fixed-point theorems and mathematical programming techniques and we show that for various variants of definitions regarding how to resolve such transitive delegations, there is always a feasible resolution; and we identify under which conditions such solutions are efficiently computable.
翻译:我们调查将液态民主纳入选民提交累积选票的选举环境的有效方法,即当每个选民被指派一个虚拟硬币,然后她可以按自己的意愿在现有的选举选项中分发。我们特别关心精细的液态民主,这意味着选民能够将部分硬币指定给一套选举备选方案,并将关于如何进一步将这一部分硬币分成这些选举备选方案的决定委托给她所选择的另一选民。我们希望这些代表团具有过渡性 -- -- 加上我们充分尊重这些代表团的目标 -- -- 意味着不一致和周期可以发生,因此我们打算找到在计算上有效的方法解决选民代表团问题。为此,我们开发了基于固定点的理论和数学方案编制技术,我们表明,对于如何解决这种过渡代表团的各种定义,总是有可行的解决办法;我们确定这些解决办法在哪些条件下可以有效地比较。