Outcome Computation

Introduction

Underlying the principles of the Agora Project (AP) is the idea that debates can be represented in a very simple directed-graph structure. Each argument (or node in graph nomenclature) and each attack (or directed edges) is also labelled with the number of agreement or disagreement votes that users place on them.

Using both the notion support originating from votes and the debate structure implied by the debate graph, AP will be able to provide a formally justifiable outcome to a debate.

Outcome computation

To obtain the outcome of a debate, we compute the social support of an argument or an attack based on the votes that users have placed on them. We then defines the outcome of a debate as a function giving each argument an "acceptability" value between 0 and 1, where 1 is completely accepted and 0 is completely refuted.

The outcome of a debate itself is a function of argument and attack social support and of the debate structure. It can be given as a solution to a system of equations, with one equation for each argument. These equations can be parametrised by using different operators. Solutions to this system of equations can also be called fixpoints of the system.

It has been proven that, for well-behaved operators, there is always a solution to a debate. It has also been shown that under some further restrictions, there is at most one solution. This means that an argument in a debate can't both be accepted and refuted.

The concrete semantics to be used must be deployed in a system and tested with a real userbase. It is expected that they will then undergo a period of revision and fine-tuning until they are acceptable for widespread use.

Advantages over current systems

The Agora Project has a few extremely important advantages over current online argumentation systems.

1. Formally justifiable outcome: many systems don't provide debate outcomes. AP does so based on both voting and debate structure.

2. Granularity: the outcome isn't about who wins or loses, but instead about which specific arguments are accepted and which are refuted.

3. Flexible debate structure: instead of the typical proponent/opponent two-side system, SAA allows any number of users to participate in any number of interconnected issues.

4. Accessibility: users decide on their level of participation. They can get more involved by proposing arguments and counter-arguments, or simply vote on arguments, thereby easily expressing their opinions.

5. Self moderation: instead of relying on moderators to effectively remove non-sensical or troll arguments, the community itself decides, by voting, which arguments actually have the social support to make a difference in the outcome.