kets using an automated market maker called a market scoring rule. This market maker is an algorithmic agent that is always willing to buy or sell securities at current market prices that depend on the history of trade. Hanson’s ideas build on the extensive literature on proper scoring rules, 20 payment rules that elicit honest predictions from agents. Market scoring rules ensure the market maker has bounded risk and that traders are unable to engage in arbitrage. Because of these desirable properties, Hanson’s market scoring rules have become the prediction market implementation of choice used by companies including Consensus Point, Inkling, and Augur, and large-scale academic projects including SciCast ( http://scicast.org) and the Good Judgment Project. 38

Recently there has been interest in further tapping into the informational efficiency of prediction markets and using them to obtain accurate predictions on more fine-grained events. For example, instead of viewing a Presidential election as having two possible outcomes (Democrat wins or Republican wins), we could view it as having 250 potential outcomes, with each outcome specifying a winner in each U.S. state. Traders could then trade securities on events (combinations of outcomes) to profit on their unique knowledge, such as whether or not the same candidate will win in both Ohio and Florida, or whether or not the Republican candidate will win in at least one of Ohio, Pennsylvania, and Virginia. Such a prediction market is called a combinatorial prediction market. Unfortunately, due to the difficulty of keeping prices logically consistent across large outcome spaces, running market scoring rules off-the-shelf is computationally intractable for many natural examples of combinatorial markets. 5

In search of pricing rules that are
tractable and preserve the logical rela-
tionships between security payoffs, Ab-
ernethy, Chen, and Vaughan1 proposed
a general framework for the design of
efficient automated market makers
over very large or infinite outcome spac-
es. They took an axiomatic approach,
defining a set of formal mathematical
properties that correspond to economic
properties that any reasonable market
should satisfy (such as “no arbitrage”
and an “information incorporation”
property) and fully characterized the set
of pricing mechanisms that satisfy these
properties. Then, using techniques
from convex analysis, they provided a
method for designing specific market
makers that satisfy these properties.
The framework enables formal reason-
ing of trade-offs between different eco-
nomic features of these market makers
as well as evaluating the computational
efficiency of the pricing algorithms.
This framework is particularly ex-
citing because it offers a way to think
about approximate pricing in combina-
torial markets when exact pricing is still
intractable. Approximate pricing for
markets is challenging because approx-
imation errors may be exploited by trad-
ers to cause the market maker to incur
a large or even infinite loss. The frame-
work of Abernethy, Chen, and Vaughan1
characterizes deviations from exact
pricing that won’t add additional cost to
the market maker. Building upon this
understanding, Dudík et al. 9 further
developed a computationally tractable
method to run a large-scale prediction
market that allows participants to trade
almost any contract they can define over
an exponentially large outcome space.
This method is starting to gain traction
in industry where it has been used in the
Predict Wise election market10 and pre-
vious and upcoming iterations of the
Microsoft Prediction Service.f
Fair division for the masses. Social
computing systems can be used to help
groups of people make decisions about
their day-to-day lives. One particularly
innovative example is Spliddit,g a web-
site that provides tools that help groups
of people achieve fair allocations. Splid-
dit currently offers tools to allocate
rooms and divide rent payments among
roommates, split taxi fares among pas-
sengers, assign credit in group projects,
divide sets of (divisible or indivisible)
goods among recipients, or split up
tasks among collaborators. It has been
featured in the New York Timesh and had
tens of thousands of users as of 2014.22

Spliddit’s website boasts “ indisputable fairness guarantees.” Indeed, each of the division mechanisms employed on the site stems from the body of re-

 

f http://nyti.ms/1sL06wt g http://www.spliddit.org/ h http://nyti.ms/1o0TUtO

Recently there
has been interest
in further tapping
into the information
efficiency of
prediction markets
and using them to
obtain accurate
predictions of more
fine-grained events.