Follow the Leader
Co-Authored by Sam Bydlon, Salil Malkan, and Marty Santalucia
We often elect or appoint leaders that represent our values; an individual who we feel reflects our views and priorities. These people are tasked with guiding our values and maintaining the day to day business of our government; there is real power in possessing both of these responsibilities. When, however, these roles are filled by two different individuals, the power dynamics become a balancing act. This post will explore how that act plays out in the Pennsylvania State Senate.
In our last post, we used voting data from the 2015–2016 Pennsylvania State House to identify Democrats and Republicans who represent the ideological cross-roads of their party. These individuals, we argued, hold stances that best represent their parties in totality. For negotiators, this is helpful insight. Understanding these individuals translates to a better understanding of what other members might be comfortable supporting. What remained unclear was whether the identified members are ideological leaders, or if they just happen to hold views that put them in this central position. We wondered, if they were to change their positions, would they maintain their centrality within the caucus? If they did, this would be evidence of them being a “true” ideological leader. However, if their centrality diminished, they may have simply held views that temporarily put them in a central position.
Our previous analysis identified that central members were often recently elected and always “rank-and-file” (meaning that they don’t hold any internally elected positions within the caucus). Perhaps the most surprising result of our previous analysis was that none, not one, of the top-ranking members in either the House or the Senate were identified as central members of their caucus. Therefore, we are suggesting that the central members were identified because they held views which were representative of the larger legislative body at the time, not that they are true ideological leaders (yet).
In the House, Democratic Leader Frank Dermody’s betweenness was only the 37th highest out of all 83 House Democrats. Speaker Mike Turzai’s betweenness was the 31st highest out of all 119 House Republicans. The landscape was similar in the Senate. Neither the Senate’s Democratic Leader, Senator Jay Costa nor President Pro Tempore, Senator Joe Scarnati (in Pennsylvania the President Pro Tempore is elected by the full Senate and is equivalent to the Speaker of the House) were identified as being amongst the most central members. Of all 19 Senate Democrats, Senator Costa’s betweenness was 5th highest and equal to 9 other Senators. President Pro Tempore Scarnati had the 5th highest betweenness out of 31 Senate Republicans. All of these leaders, however, are still tasked with moving their caucus toward legislative goals. Their challenge, and what we will explore here, is how they accomplish that objective from a suboptimal position within the network.
The Senate Democrats are the smallest caucus with 19 members, so let’s focus on this body for now to keep things simple. There are a handful of metrics within our network that we can use to identify the source of a leader’s influence. These metrics include:
- Betweenness centrality: A measure of how often a member sits on the shortest path between other members.
- Degree centrality: A member’s degree centrality is defined by how many other members are directly connected to them. This cluster is often referred to as a neighborhood with the member we’re focusing on in the center and the others branching off like a snowflake. We say that the larger a member’s neighborhood, the more “popular” they are.
- Relationship strength: Referred to as “edge weight” in network analysis; we assign every relationship a value from 0% to 100% that corresponds with how often those members vote together. Our networks only use relationships that are stronger than the average of the entire population.
What we know for sure, is that internally elected leaders are given certain political benefits, such as a seat at the table when negotiating legislation with the Governor and other internally elected leaders. Generally, we’re hypothesizing that these political benefits are quantifiable through the use of network analysis. Our methodology from our last post identified ideological centers using betweenness centrality. As you can see in Figure 1 above, Senator Costa was not identified as a central member. He simply isn’t much of a bridge in the network. He may, however, be able to compensate for that with “popularity”.
If an internally elected leader’s influence isn’t coming from their betweenness, they may be able to leverage an unusually large neighborhood. We hypothesize that internally elected leaders could be the most “popular,” i.e. they are the individuals that have the highest number of relationships within the network (and thus the highest degree centrality). Our idea is that the internally elected leaders may use their many connections to distribute their influence more widely.
There really isn’t much we can get from this network. The network has a density of 71%, which means that of all possible relationships between members, 71% of them are actually present. This is an intuitive result, since members of the same party are likely to have relationships with each other. Our analysis shows many Senators with roughly the same degree centrality. With 15 relationships, Senator Costa doesn’t stand out. If our graph withheld names, we wouldn’t be able to pick him out from the other 18 Senators that have 12–16 relationships. We reject our hypothesis that internally elected leaders are amongst the most “popular” members. Incidentally, this result indicates that other degree-based methods of analysis, such as eigenvector centrality, will hold limited value in this investigation.
Fortunately, we have other ideas. Let’s hypothesize that even though Senator Costa doesn’t have more connections (or higher degree centrality) than the average Senator, it is possible that he is connected to Senators who together have a higher average of betweenness centrality. In practice this theory would indicate, that if an internally elected leader needed to whip votes for a particular bill, he/she would be able to sell the legislation to his/her allies. Those allies, in turn, would use their more central positions in the network to move votes within the caucus.
To test this hypothesis, we looked at each Senator and averaged the betweenness of everyone they were connected to. We call this measure “Average Neighborhood Betweenness” (ANB). To determine if the ANB of each Senator is statistically higher or lower than the average of the entire caucus, we used a normal analysis of means. Results of the analysis are shown in Figure 3. The green line denotes the average betweenness of the entire caucus and the red lines denote the upper and lower “decision limits.” If a Senator’s ANB is outside of the decision limits, we can say with 95% confidence that there is a statistically significant difference between the Senator’s ANB and the average betweenness of the entire caucus. Another way of saying this, is if a Senator’s ANB is outside of the decision limits, we know their neighbors are significantly more or less central than average. We performed this analysis on every Democratic Senator.
According to our analysis, Senator Costa’s ANB is roughly average. In fact, no Senator had an ANB that stood out from the pack. This means that Senator Costa’s neighbors are not significantly more central than any other Senator. Yet again, we reject our hypothesis.
The last hypothesis we focused on was the strength of the relationships Senator Costa had with those around him. Every relationship has value between 0% and 100%, which was computed based on how frequently two members vote with each other. This is the strength of the relationship. It can also be used to quantify how efficiently influence travels between any two Senators; the higher, the better. The average relationship within the Senate Democrats’ network is 97.2% with a standard deviation of 1.1%. If two members vote with each other greater than 99.5% of the time (two standard deviations above the mean), we say that the relationship has high efficiency. If two members vote with each other less than 94.9% of the time (two standard deviations below the mean), we say that the relationship has low efficiency.
We know Senator Costa doesn’t have more relationships than the average Senator, but it is possible he has stronger relationships. Being able to move his influence more efficiently to his immediate neighbors would give him a head-start in the network. We tested our hypothesis in a similar manner to how we tested ANB; we averaged the strength of Senator Costa’s relationships and compared them to the entire caucus. Figure 5 shows the results.
Nothing. If anything, Senators Blake and Wozniak might want to work on their positioning since we found that their relationships were statistically weaker than we would expect them to be. For Senator Costa though, he’s right around average. Another hypothesis rejected; the struggle of science.
We set out to explore and better understand what makes internally elected party leaders in the PA state legislature tick. The people in these positions are charged with influencing members of their caucuses in order to achieve the legislative agendas of their parties. So how do they do it? Do these individuals have larger networks they leverage? Are their connections, on average, more central? Based on the way members vote, it doesn’t look like it. When it comes to influencing the caucus to make a particular choice, the leader doesn’t appear to be particularly powerful.
To check this result, we went back and performed the same analysis for other internally elected leaders in the Senate and House. Our results were the same across the board with one exception; Republican House Speaker Turzai’s relationship strength is statistically higher than the average Republican house member. The average relationship strength of Speaker Turzai’s neighborhood was 94.7%, which was higher than the upper decision limit of 93.3%. In 12 separate analyses (all three hypotheses above tested for all combinations of the House/Senate and Democrat/Republican caucuses), this was the only internally elected leader that stood out statistically.
One possible explanation for how elected leaders get things done, is that official leadership positions arm the elected leader with a very powerful tool — agenda setting. Party leaders get to decide what options the other members have to choose from (in terms of bill content), through old-fashioned politics and negotiating, and that’s where their real power comes from.
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Sam Bydlon: email / twitter
Salil Malkan: email / twitter
Marty Santalucia: email / twitter
