coming the leader for such processes in the U. S.e For example, this platform was recently used to decide how to spend $250,000 of infrastructure funds to improve Long Beach (CA) Council District 9, and how to allocate $2.4 million of Vallejo’s capital improvement budget. Looking forward, it is an interesting and open research challenge to understand if these algorithms and systems yield near-optimal aggregations of societal preferences, or decisions that are near-optimal in terms of overall societal utility.

Automated market makers for prediction markets. A prediction market is a financial market designed to extract and aggregate predictions from a crowd. In a typical prediction market, traders buy and sell securities with payments that are contingent on the outcome of a future event. For example, a security may yield a payment of $1 if a Democrat wins the 2016 U.S. Presidential election and $0 otherwise. A trader who believes the true probability of a Democrat winning the election is p maximizes his expected utility by purchasing the security if it is available at a price less than p and selling the security if it is available at a price greater than p. The market price of this security is thought to reflect the traders’ collective belief about the likelihood of a Democrat winning.

Prediction markets have been shown to produce forecasts at least as accurate as other alternatives in a wide variety of domains, including politics, business, disease surveillance, entertainment, and beyond, and have been widely cited by the press during recent elections. However, markets operated using traditional mechanisms like continuous double auctions (similar to the stock market) often suffer from low liquidity. Without liquidity, a market faces a chicken-and-egg problem: potential traders are dissuaded from participating due to lack of counterparties, which contributes to an even greater reduction in future trading opportunities.

Low liquidity can also lead to high price volatility and large spreads, both of which cause the market price to yield a less meaningful prediction.

To combat this problem, Hanson23
proposed the idea of operating mar-
e https://pbstanford.org/cambridge/approval
prediction markets, 1, 2, 33 human com-
putation games, 28, 39 and user-generated
content sites; 12, 15, 17, 29 see, for example,
Ghosh14 for a survey of one facet of this
work. However, we are far from having
the systematic and principled under-
standing of the advantages, limitations,
and potentials of social computing re-
quired to match the impact on applica-
tions that has occurred in other fields.

We note that social computing enjoys a close relationship with another emerging discipline, which is computational social science. 19, 34,a But it is also distinct from that field. While human and social behavior, ability, and performance are central to both, computational social science focuses primarily on the use of modern technology, data, and algorithms to understand and describe social interactions in their “ natural habitats.” In contrast, social computing (as the name suggests) has a much more deliberate focus on engineering systems that are hybrids of humans and machines, which may often entail shaping collective behavior in unfamiliar environments. Nevertheless, we anticipate a continued close relationship and even blurring of the two efforts. As an example, one should expect the vast theoretical and experimental literature on the diffusion of influence and behavior in social networks to be relevant to any effort to design a social computing system that relies on such dynamics to recruit and engage workers.

In June 2015, we brought together roughly 25 expertsb in related fields at a CCC-sponsored Visioning Workshop on the Theoretical Foundations of Social Computingc to discuss the promise and challenges of establishing mathematical foundations for social computing. This document captures several of the key ideas discussed.

Success Stories

We begin by describing some examples in which mathematical research has led to innovations in social computing.

Crowdsourced democracy. YouTube competes with Hollywood as

a There are also clear connections to, and influence
from, older topics and models in the classical
mathematical sociology literature. 6
b Participant list and bios available at http://bit.ly/
1Vy9Ck7.
c http://cra.org/ccc/events/theoretical-founda-
tions-forsocial-computing/
an entertainment channel, and also
supplements Hollywood by acting
as a distribution mechanism. Twit-
ter has a similar relationship to news
media, and Coursera to universities.
But Washington has no such counter-
part; there are no online alternatives
for making democratic decisions at
large scale as a society. As opposed to
building consensus and compromise,
public discussion boards often devolve
into flame wars when dealing with con-
tentious socio-political issues. This
motivates the problem of designing
systems in which crowds of hundreds,
perhaps millions, of individuals col-
laborate together to come to consen-
sus on difficult societal issues.
Mathematical research has recent-
ly led to new systems implementing
crowdsourced democracy. 21 This work
builds upon a body of research on so-
cial choice that examines how to best
take the preferences of multiple agents
(human or otherwise) and obtain from
them a social decision or aggregate so-
cial preference, typically accomplished
through some form of voting.d
d A significant research community concerns
itself primarily with computational social
choice: 4 This area has particular promise for so-
cial computing because of the problems of scale
that are associated with group decision-making
online, such as in crowdsourced democracy.