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Aziz provides a good definition of this academic discipline.
Computational Social Choice (COMSOC) is a multidisciplinary research field that combines ideas, models, tools, and techniques from both traditional social choice theory as well as computer science. On one side is classical social choice theory that involves a formal and axiomatic approach towards the problem of achieving socially optimal, fair, or stable outcomes by aggregating agents’ preferences in a suitable manner. Representative social choice settings include voting and allocation problems. Since many multi-agent settings within computer science such as ranking systems, crowdsourcing, cloud computing, and two-sided matching markets involve similar concerns, social choice theory has provided a groundswell of ideas to model strategic scenarios in mult-agent settings and formalize fairness and welfare. On the other hand, there are many important problems in social choice that require computational consideration to build scalable systems. Computer science with its toolkit of optimization techniques, tradeoff analysis, and algorithm design is ideal to tackle such problems.
Computational Social Choice: Some Current and New Directions (Aziz)
I believe this literature treats rigorously many questions raised by the political theory of economic planning, though this is rarely intentional. Most directly relevant are voting algorithms for participatory budgeting.
What follows are a collection of links that seem like they could be relevant to a discussion of socialist economic planning protocols, or which would help me gain the prerequisites needed to understand papers relevant for that project.
Peters - Participatory Budgeting Survey
Irfan - CSCI 3210: Computational Game Theory (Ford-Fulkerson applied to Fisher markets)
Irving Fisher's hydraulic market equilibrium computer
Fleischer - A Fast and Simple Algorithm for Computing Market Equilibria