## Why range voting is "uniquely best" among all common proposals for single winner
voting systems

For the
Bayesian-regret
measurement study via massive computer election simulations
using many election systems, see paper #56
here.

Here is some typical data from that study.

**Regret measurements. **
Column A: 5 candidates, 20 voters,
random utilities;
Each entry averages the regrets from 4000000
simulated elections.
Column B:
5 candidates, 50 voters,
utilities based on 2 issues,
each entry averages the regrets from 2222222
simulated elections.
Voting system |
Regret A |
Regret B |

Magically elect optimum winner |
0 |
0 |

Range (honest voters) |
0.04941 |
0.05368 |

Borda (honest voters) |
0.13055 |
0.10079 |

Approval (honest voters) |
0.20575 |
0.16549 |

Condorcet-LR (honest voters) |
0.22247 |
0.14640 |

IRV (honest voters) |
0.32314 |
0.23786 |

Plurality (honest voters) |
0.48628 |
0.37884 |

Range & Approval (strategic exaggerating voters) |
0.31554 |
0.23101 |

Borda (strategic exaggerating voters) |
0.70219 |
0.48438 |

Condorcet-LR (strategic exaggerating voters) |
0.86287 |
0.58958 |

IRV (strategic exaggerating voters) |
0.91522 |
0.61072 |

Plurality (strategic voters) |
0.91522 |
0.61072 |

Elect random winner |
1.50218 |
1.00462 |

As you can see, Range voting has a lot smaller Bayesian regret than the other systems.
Note: this table makes it appear that Borda is the second-best system after
range. But in fact the full study considers about 100 tables of this kind,
and in many of them, Borda is *not* second best, in fact in many of them
it is way down in the rankings. The question of which system is second best
has no clear answer - some of them are better in some kinds
of election situations, others in others. But range voting *always* came
out best (or at least tied for best) in *all* the tables.

### How big an improvement is this?

Huge. In this (and other) tables, reduction in regret you get from switching to range is
instead of plurality is a *factor* of 7-10 for honest voters and
2-3 for strategic ones.

That was larger than the
improvement in regret we got by switching from non-democratic systems such as
monarchy (we assume monarchs, on average, were as least as good rulers as
a random candidate, since, e.g. they were trained from birth to rule), to plurality:
only a factor of 2-4 for honest voters and about 1.6 for
strategic voters.

Also, if you do not like multiplicative factors - you like additive differences -
then the improvement we got from switching from random winner to (our
current) strategic plurality
is comparable to the improvement we will get from the future switch to
range voting with a mixture
of honest & strategic voters.

In other words **you get comparable or more improvement
in democracy by switching from plurality to
range voting, than you get from the very invention of democracy in the first place.**