# Beyond Voting

~ *we might escape strategic votes, in the land of machine intelligence *~

**TL;DR** — Voting seemed cursed since the 70’s, due to Gibbard’s Theorem, that any voting method is unfair in one way or another: dictatorial, strategic, or it gives only two choices. Well! As far as I can tell, Gibbard only seems to apply to ranked lists… while Machine Intelligence research shows that our algorithms are more competent when given **vectors** in a ‘high-dimensional latent space’ **instead**. Gibbard’s Theorem does NOT apply to such a data-type, and so that region of algorithms *MIGHT* hold a strategy-proof and collegiate voting system! I sketch the arguments for such a method, below.

**Gibbard’s Bane**

In 1973, Allan Gibbard expanded upon the intuitions of fellow researcher William Vickrey — to use Arrow’s Impossibility Theorem to prove that no voting system escaped strategic votes, unless only one or two controlled all. So much for a ‘more perfect union’!

And there we have sat, for 48 years. Yet, look at Gibbard’s phrase, explaining what must come *first* for a ‘trick’ ballot to yield better results for the person casting it: “Both a constitution and a voting scheme take **preference n-tuples** as arguments” (p.592, 3rd parag. *emph. mine*) “Preference n-tuples” are ranked lists; your first pick down to your least favorite.

And, let’s be clear — whenever you have ONLY this **preference-list**, then yes, Gibbard says there is no fair vote. (Choose Among: Strategic, Dictatorial, or Two-Options Only) Yet, that formulation of the problem* cannot make any claim upon *the case where each person’s preferences are expressed as ** a vector in a high-dimensional latent space** (the kinds used by Variational Auto-Encoders and Transformers, those new-fangled A.I.).

Sure, that high-dimensional vector **can be converted down** to a preference-list, yet that conversion *throws-away almost all the important information*! When we want an algorithm to perform well, we can’t *declare failure* after denying it sufficient information. Consider the real-world examples in proven A.I. applications: A Variational Auto-Encoder takes an image (for instance) and converts that into a ‘*latent-space vector*’… which it can then convert back into the original image, successfully. **Given all the information it needed, it was able to function properly**. That ‘latent-space vector’ was holding-onto all the important information, and THAT is why the VAE could reconstruct the input. However, you can ask any ML researcher: “*If we convert those latent-space vectors into **scalars**, to form an **ordered list**, will we still be able to reconstruct the input?*” **No, they will explain, because you threw-out all the important data when you converted a vector into a scalar**.

Similarly, Transformers rely entirely upon their key and query vectors’ **orientation**. If you took the *scalar length of each*, or any distance metric, then they become meaningless. No, we *cannot* expect our best algorithms to fail with the **best data**, just because Gibbard’s algorithms fail when he gave them **collapsed data**. We simply do not know either way, at this moment.

**Hints?**

There are some vague intuitions to believe that Gibbard’s Theorem won’t hold for latent-space vectors and machine intelligence: with loss-minimization, such spaces are provably convex, doomed to succeed. A formulation of ‘minimal regret’ would seem to follow the same constraints. More importantly, consider what happens to someone’s ‘vote’ when they are strategic, and how that is portrayed and dealt-with in a latent-space:

Suppose **Voter A **wants Bernie Sanders to win, using a new voting system we decide to try. Yet, **Voter A**’s second-favorite, Kucinich, is more *likely* to win! So, to be *strategic*, **Voter A** places Kucinich at *the bottom of their ballot*, ‘claiming’ falsely that he is their least favorite. And this lie is enough to bring Kucinich down, letting Bernie win. A strategy!

Yet, if voters’ preferences are projected onto a high-dimensional latent-space, then they are **naturally ‘clustered’ by similarity**. So, that one **Voter A**, with Bernie at the top of their ballot and Kucinich at the very *bottom* (below Ted Cruz?!?) would be placed OUTSIDE all the normal clusters! “Weirdo. Obviously some kind of fraud or delusion,” say the clusters. And, if the method for *settling on an elected choice *tends toward a broad ‘mode’ among those clusters, then that ‘strategic’ vote is given LESS weight in the outcome.

**That ‘mode-seeking’** is the key insight for how to design a cluster-based method which might prevent strategic voting, in its entirety: “*the best outcome for you will happen when you are honest*.” **Because strategic votes are idiosyncratic, they are first to be ignored**.

How do we find those clusters, from the voters? Machine Intelligence, again — it can read** detailed interviews** and** longitudinal surveys** from each person, **encrypted homomorphic records of their voting history**, aggregations of **concerns** and **interests**. Put all that together to form the ‘profile’ of each voter, which the Variational Auto-Encoder places somewhere in its cupboard of clustered vectors. If someone wants to ‘vote strategically’, then they must *plan long in advance* to **fake their entire history** up to that point, *if only to fool Kucinich ONCE*. That sounds unlikely.

So, there are compelling reasons to ** check** if a voting system

**succeed by using latent-space vectors, despite the fact that Gibbard proved all**

*might**preference-orderings*will fail. A “failure of algorithms upon the

**preference-ordering**” does NOT imply a “failure of algorithms upon the

**latent-space vectors**.” A new vista is open to us.