Rumor Has It

EE376A (Winter 2019)

Authors: Brandon Benson, Stephen Spears, Eric Gong

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Our project is an exploration of how ideas spread and become embedded. We are interested in synthesizing the spread of ideas throughout society with a model of information transfer. The inspiration for our project began with the model presented by Wang, et. al. in “A Rumor Spreading Model Based on Information Entropy”. We initially implemented the model and qualitatively matched the results from their paper. From that point, we created a parsimonious version of the model. Casting this parsimonious model in terms of channel coding, we abstracted the encoding process, allowing for any encoding that corresponded with the channel size defined by the Binary Symmetric Channel (BSC) framework. With this model in hand, we aim to augment dynamic, social opinion data with information concepts, namely in US Presidential Election voting data. We are interested in applying our current model’s ability to describe the spreading of information to the domain of Presidential Election and modeling the change of voting patterns throughout US counties over the course of Presidential Elections. County-wide voting data of the past five US presidential elections gives the fundamental information that is being spread over the course of time. We want to demonstrate that our model will account for this spread of political information and how particular counties influence one another in how they vote. The goal is to create a directed information visualization that illustrates how voting trends spread from county to county.

As a case study, we focused on the 58 counties in the State of California in this millennium. We constructed a network of California with counties as nodes, training channels between counties that yielded a model steady state corresponding with voting data.

With this model, we generate the distribution of opinions held by the county. We compare these distributions between counties and compute mutual information empirically. Doing this during steady state and during transitions between election years reveals two different phases of information spread. During the steady-state phase, individual counties have high entropy, but there is little mutual information between the counties. During the transition phase, individual counties have low entropy, but mutual information between counties is much higher. This indicates an increased flow of information between counties during the transitions between election years. Furthermore, we see a clear increase in mutual information across the entire state.

interperiod

For the 2012 and 2016 steady states (left and right) we see very low mutual information between counties, but high entropy (diagonal). This steady state phase is markedly different from the transition phase in which mutual information between counties is much higher, but entropy is low

Looking at the maximum eigenvalue of the MI matrix gives us a measure of how inter-connected the counties are becoming.

most virulent

Computed Mutual Information between counties over the transition period between presidential election years on the left while predictions using the four previous election year transitions on the right

Using linear regression, we predict the transition mutual information from2016 to 2020, highlighting the counties that have the strongest mutual information with the whole state (lower right), calling these “virulent”. While our model is informed only by geography and election data, it identifies intuitively virulent counties such as Los Angeles, Napa, and San Francisco. As expected, the inter-connectedness of these counties is very high. Using this mutual information, political campaigns can better strategize which counties to focus on to win the entire state of CA

In the same figure, we use Google Maps to plot the virulent counties.

eigen

With this model, we interpolate between election years, studying the mutual information between counties. The development of this mutual information over time elucidates trends which are consistent with intuition. More specifically, however, we highlight virulent counties which we predict to be critical for 2020 campaigning. Specifically, we hope to contribute towards a richer understanding of voting data, beyond static measures to the domain of channel coding and more generally information theory.

Outreach:

Our outreach project was a variation on the popular party game Telephone. In Telephone, one person thinks of a sentence and whispers it to the person next to them. This next person then whispers the message they heard to the person next to them. And so, the message passes around in a circle in this way until it reaches back to the original person. Our variation was to create a direct graph on the ground using masking tape. Every player in the game would start at a node of the graph and then would whisper the message they heard to the people connected to them by a directed edge. In a four-player game—the minimum number required for this game—a person would be designated as the message originator. He or she would think of a fun sentence and then whisper it to the people that they were connected within the graph. As soon as these neighboring players heard this message, they would be required to pass on the message to their neighbors. After a couple of minutes of this information flow, we would stop the game and ask the players to list all the different sentences they had heard throughout the course of the game. Players frequently named as many as three or four different sentences, many of them being different versions or variations of each other. Sometimes a message was misheard, sometimes it was misremembered, sometimes people just wanted to be mischievous. The goal of the game was to illustrate that due to a noisy channel (i.e., hurried whispers to one another in a noisy room), there would be different errors and variations that arose as a result. Entropy describes this process and how it would affect the accurate spread of information. The game served as a microcosm for how information and rumors are usually spread. The hope was that the kids would have a concrete, and hopefully memorable, first-hand experience of these information theory concepts, and that they would have a better appreciation for how rumors may be spread.

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