will design and implement algorithms that use and track human inputs to evolve new opinions and to evaluate existing ones (we will refer to these as "genetic algorithms" in the next pages. This process can be structured in several ways. We are currently considering two basic, alternative (but possibly complementary) structures: one in which users interaction is carried on sequential discrete rounds, and one in which the interaction is continuous over the time. Different aggregation criteria can be used for different approaches.
We now describe the procedure carried on discrete rounds. The process will proceed through rounds of subsequent generation of new opinions, and endorsement and evaluation of existing opinions. We shall define that an opinion A dominates an opinion B if all the users that have endorsed B have also endorsed A, plus some other users (see Figure 1). Note that in this regard we are not counting votes, but effectively considering which user has endorsed what, and confronting those sets of users opinions.
Figure 1 - Opinion A dominates opinion B
The procedure works as follows. We start by asking people to write their opinions in regard to a certain issue (Round 1.A). We then ask everybody which set of opinions they wish to endorse (Round I.B). Once each user has cast her endorsement, we archive all the opinions dominated by other opinions, thus remaining with a Pareto front of opinions (i.e. a set of opinions where no opinion dominates another one, see Figure 2). We consider those opinions as the winning strategies of this round, say win. We then use the opinions in win to seed the next round. Next, we present win to the users as the set of surviving opinions, and we ask them to write new opinions, possibly trying to integrate-i.e. defining a new opinion dominating one or more old opinions-different existing opinions (Round 2.A). We then ask the users to endorse all the opinions they agree on (Round 2.B), compute the Pareto front of the result and assigning it to win (Round 2.C), and so on and so forth. Although the process seems to be well defined, there is a consistent research that needs to be done. For example, as defined here, the procedure only would end when the users have reached complete unanimity in their opinion. A different halting form needs to be defined. Also we need to test how successful such process is respect to real life issues.
Figure 2 - Pareto front for a set of opinions
We now describe the procedure evolving on continuous time. A second possible process that we intend to investigate for the synthesis of group knowledge does not go through discrete time steps like the approach just described. Instead, in each instant all users can read the existing opinions, endorse the opinions that they agree on, and produce new opinions. Sometimes those opinions will be refinements of existing ones, in which case the new opinion will compete against its predecessor. Nonetheless, this would be a very unfair competition, as the new opinion will start later with fewer votes. In order to balance the unfairness of this situation, various possibilities can be tried and investigated. For example, we can sample the users endorsing the first proposal, if they endorse also the second one. Based on the result of this sampling we should be able to predict what would be the second opinion's relevance. We should then advertise the opinion based on the