# 4

The manipulation problem, in short, is when a speculator privately benefits from a particular decision  and hence is willing to buy excessive conditional stock  so that  is enforced. I've heard Robin Hanson explaining that other speculators will react to counter manipulation but I'm not sure I get how it's supposed to work in practice:

Suppose that the optimal decision is  and denote  as the expected value of one conditional stock  (given that  is enforced). The rational, risk-neutral & disinterested speculators will pay at most  for each  .

If a speculator receives a private benefit  when  is enforced, she'd be willing to  pay  for  conditional stocks , or   for each . It seems to me that given finite stocks and a large enough , the conditional price of  might outweigh that of the optimal decision  (i.e.)

A counter to my description is that speculators can also short-sell, but short-selling (at least currently) involves borrowing existing stocks and selling them, whereas in futarchy the manipulator can simply refuse to lend stocks to short-sellers. In addition, if only one speculator receives the private benefit , then short-selling   to other investors would only gain  in revenue, which undermines the incentive of short-selling in the first place.

Is my analysis wrong? Or is there some other mechanism to counter market manipulation?

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JBlack

### Dec 21, 2021

6

In most models of prediction markets that I've seen so far, stocks aren't finite. Any investor can pay to create an outcome-neutral bundle.

If the benefiting speculator is willing to pay more than E(D) for a D stock, then other investors can create more and sell D to that buyer for a price greater than E(D) while holding or selling off the rest for net expected profit. In most cases this will result in a price somewhere between E(D) and E(D*).

If E(D*) and E(D) are very close, or the D buyer financially dominates the whole market, then this could still result in market manipulation such that price(D) > E(D*). In the former case, there's an argument that the correct decision really is D rather than D*: the expected loss to the public is tiny while the benefit to the single person (or perhaps minority coalition) is great enough to outweigh the combined difference to the rest of the market.

The second case is more problematic, but really if a single entity already dominates the markets to that extent, there are other problems.

Would there be a problem when speculators can create stocks in the conditional case? As in if a decision C harms me, can i create and sell loads and loads of C stock, and not having to actually go through the trade when C is not enforced (due to the low price i've caused)?

1JBlack6mo
In the simple conditional case with N possible outcomes, you are (in the basic case) paying $1 to create 2N stocks: W|D_i and (1-W)|D_i for each of the N decisions D_i, where W is the agreed welfare metric ranging from 0 to 1. When decision n is implemented and the outcome measured, the W|D_n and (1-W)|D_n stocks pay out appropriately. So yes, if you never sold your |D_n stocks then you get$(W + 1-W) = \$1 back. However, you don't have an unlimited number of dollars and can't create an unlimited number of stocks.