# [EM] VSE graph... with SODA!

Jameson Quinn jameson.quinn at gmail.com
Thu May 29 17:06:46 PDT 2014

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As before, the x axis is honest VSE, the Y axis is one-sided strategic VSE,
and the bubble size is two-sided strategic VSE. SODA is looking pretty
dominant here. This is based on 1000 runs of a 2+1D chinese restaurant
spatial model.

"Honest" SODA voters delegate to their favorite iff their favorite's
preferences, expressed as ordinal integers, and not including the favorite
themselves, correlate positively with their utilities. Otherwise, they
approve down to their average utility. In practice, over 95% of them
delegated with this voter model, which is not surprising in a spatial
model.

"Strategic" SODA voters delegate iff they agree with their favorite about
the ordering of the two frontrunners; otherwise, they approve all
candidates they prefer to their less-preferred frontrunner. In practice, I
didn't keep numbers, but I'd guess that around 80-90% of strategic voters
delegated.

Candidates, when assigning delegated votes, do so based on the minimax
winner of the condorcet matrix constructed by combining all direct and
already-delegated approvals with all pending delegations. In theory, this
is not precisely the same as perfect rational strategy, but constructing a
counterexample is so hard that I'd bet that it wouldn't happen by chance
even once, even if I had run an order of magnitude more elections.

So, SODA looks pretty good here. It's a bit hard to see from the graph, but
its two-sided-strategy VSE is actually the best of any of these systems:
89.2%, as opposed to 88.2% for Score. The crossover, where Score dips below
SODA, happens as strategy increases past about 75%. That's a plausible
real-world number to me (for Score, I'd believe anything from about 40-90%
strategy; for SODA, I'd actually expect more like only 10-20% strategy, but
it basically doesn't matter either way.)
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