Using Networks to Detect Alliances and Leaders in Survivor
https://arxiv.org/pdf/1803.01783.pdf
Dynamic Competition Networks: Detecting Alliances and Leaders by A. Bonato et al.
In this paper, networks are used to analyze the relationships and voting alliances among the players in the social strategy game Survivor. In this reality show, players compete to be the last survivor standing and win the million-dollar prize. They are split into tribes that compete in challenges, with the winning tribe winning immunity, and the losing tribe being forced to vote off a player. A common strategy in the game is to form alliances with other players, and work together to vote off players who are outside the alliance.
To represent the competition with a graph, each player is represented by a node. Directed edges are used to indicate votes, connecting node A and node B if player A casted a vote against player B. As such, edges represent negative relationships. This is like the example we discussed in class where opposing countries in wars were connected with negative edges. While it is common to focus on positive relationships when trying to study the dynamics of a network, negative relationships can also be helpful in exposing who is working with who. This brings up the idea from the Structural Balance Theory that enemies of enemies are more likely to be friends. In Survivor, two people that continuously cast votes against the same people, and thus both have directed edges to those people, are likely to be working together in an alliance and have an implicit positive tie with each other.
These graphs can be used to analyze alliances and predict winners. Some of the metrics that the authors used to compare nodes were:
- indegree (the number of edges directed in) and outdegree (the number of edges directed out)
- the number of common-out neighbors (CON) where w is a common out-neighbor of u and v if (u, w) and (v, w) are directed edges
- closeness (a measure of centrality based on the lengths of the shortest paths between the node and all other nodes)
- edge density (ratio of directed edges present/ total possible edges, similar to our clustering coefficient calculation) and near independence (small edge density within a set of nodes)
The authors were able to find that strong alliances tended to have lower edge densities and formed near independent sets. This makes sense because members belonging to a strong alliance are less likely to vote for each other since that would risk their own security in the game. Another trend that the authors found was that there was a strong correlation between having a high CON score and winning. For example, 68.6% of winners had a top 3 CON score in their season, and 94.3% had a top 5 CON score. This means that players were on the right side of the vote the majority of the time and were a big influence in controlling who went home were more likely to succeed in the game.