### Abstract

This formalisation contains the proof that there is no anonymous Social Choice Function for at least three agents and alternatives that fulfils both Pareto-Efficiency and Fishburn-Strategyproofness. It was derived from a proof of Brandt et al., which relies on an unverified translation of a fixed finite instance of the original problem to SAT. This Isabelle proof contains a machine-checked version of both the statement for exactly three agents and alternatives and the lifting to the general case.

### License

BSD License

### Topics

- Mathematics/Games and economics

### Session Fishburn_Impossibility

- Social_Choice_Functions
- Fishburn_Impossibility

### Depends on

- Randomised Social Choice Theory

### Auto-related entries

- The Incompatibility of SD-Efficiency and SD-Strategy-Proofness

## Cite

×

Fishburn_Impossibility-AFP

    @article{Fishburn_Impossibility-AFP,
      author  = {Felix Brandt and Manuel Eberl and Christian Saile and Christian Stricker},
      title   = {The Incompatibility of Fishburn-Strategyproofness and Pareto-Efficiency},
      journal = {Archive of Formal Proofs},
      month   = {March},
      year    = {2018},
      note    = {\url{https://isa-afp.org/entries/Fishburn_Impossibility.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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Older releases:

- Sep 13, 2023 : Isabelle2023
- Oct 27, 2022 : Isabelle2022
- Dec 14, 2021 : Isabelle2021-1
- Feb 23, 2021 : Isabelle2021
- Apr 18, 2020 : Isabelle2020
- Jun 11, 2019 : Isabelle2019
- Aug 16, 2018 : Isabelle2018
- Jun 10, 2018 : Isabelle2017
- Mar 23, 2018 : Isabelle2017