Python Programming In this lab, we will represent a US senator’s voting record a
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Python Programming
In this lab, we will represent a US senator’s voting record as a vector over R, and will use dot-products to compare voting records. For this lab, we will just use a list to represent a vector.
2.12.1 Motivation These are troubled times. You might not have noticed from atop the ivory tower, but take our word for it that the current sociopolitical landscape is in a state of abject turmoil. Now CHAPTER 2. THE VECTOR 135 is the time for a hero. Now is the time for someone to take up the mantle of protector, of the people’s shepherd. Now is the time for linear algebra. In this lab, we will use vectors to evaluate objectively the political mindset of the senators who represent us. Each senator’s voting record can be represented as a vector, where each element of that vector represents how that senator voted on a given piece of legislation. By looking at the difference between the “voting vectors” of two senators, we can dispel the fog of politics and see just where our representatives stand. Or, rather, stood.
2.12.2 Reading in the file As in the last lab, the information you need to work with is stored in a whitespacedelimited text file. The senatorial voting records for the 109th Congress can be found in voting record dump109.txt. Each line of the file represents the voting record of a different senator. In case you’ve forgotten how to read in the file, you can do it like this: >>> f = open('voting_record_dump109.txt') >>> mylist = list(f) You can use the split(·) procedure to split each line of the file into a list; the first element of the list will be the senator’s name, the second will be his/her party affiliation (R or D), the third will be his/her home state, and the remaining elements of the list will be that senator’s voting record on a collection of bills. A “1” represents a ’yea’ vote, a “-1” a ’nay’, and a “0” an abstention.
Task 2.12.1: Write a procedure create voting dict(strlist) that, given a list of strings (voting records from the source file), returns a dictionary that maps the last name of a senator to a list of numbers representing that senator’s voting record. You will need to use the built-in procedure int(·) to convert a string representation of an integer (e.g. ‘1’) to the actual integer (e.g. 1).
2.12.3 Two ways to use dot-product to compare vectors Suppose u and v are two vectors. Let’s take the simple case (relevant to the current lab) in which the entries are all 1, 0, or -1. Recall that the dot-product of u and v is defined as u · v = % k u[k]v[k] Consider the kth entry. If both u[k] and v[k] are 1, the corresponding term in the sum is 1. If both u[k] and v[k] are -1, the corresponding term in the sum is also 1. Thus a term in the CHAPTER 2. THE VECTOR 136 sum that is 1 indicates agreement. If, on the other hand, u[k] and v[k] have different signs, the corresponding term is -1. Thus a term in the sum that is -1 indicates disagreement. (If one or both of u[k] and v[k] are zero then the term is zero, reflecting the fact that those entries provide no evidence of either agreement or disagreement.) The dot-product of u and v therefore is a measure of how much u and v are in agreement.
2.12.4 Policy comparison We would like to determine just how like-minded two given senators are. We will use the dot-product of vectors u and v to judge how often two senators are in agreement.
Task 2.12.2: Write a procedure policy compare(sen a, sen b, voting dict) that, given two names of senators and a dictionary mapping senator names to lists representing voting records, returns the dot-product representing the degree of similarity between two senators’ voting policies.
Task 2.12.3: Write a procedure most similar(sen, voting dict) that, given the name of a senator and a dictionary mapping senator names to lists representing voting records, returns the name of the senator whose political mindset is most like the input senator (excluding, of course, the input senator him/herself).
Task 2.12.4: Write a very similar procedure least similar(sen, voting dict) that returns the name of the senator whose voting record agrees the least with the senator whose name is sen.
Task 2.12.5: Use these procedures to figure out which senator is most like Rhode Island legend Lincoln Chafee. Then use these procedures to see who disagrees most with Pennsylvania’s Rick Santorum. Give their names.
Task 2.12.6: How similar are the voting records of the two senators from your favorite state?
Explanation / Answer
myvoted_data = list(open("myvotingfile.txt"))
Task 2.12.7
def find_avg_sim(senator, senator_set, v_dict):
The inputs are the name of the senator, a set of senator names and a vote dictionary
The output is the average dot product between senators and a set of senenators
return sum([poll_comp(senator,k,v_dict) for k in senator_set])/len(senator_set)
def poll_compare(senator_a, senator_b, v_dict):
return sum([v_dict[senator_a][k]*v_dict[senator_b][k] for k in range(len(v_dict[senator_a]))])
Task 2.12.8
def my_avg(senator_set, v_dict):
The inputs are the name of the senator, a set of senator names and a vote dictionary
The output is the average dot product between senators and a set of senenators
The inputs are a set of senator names, a voting dictionary
The output is a vector containing the average components of the voting records of the senators
ie vector addition on the lists representing their voting records, and then divide the sum by the number of vectors
return [sum([v_dict[senator][k] for senator in senator_set])/len(senator_set) for k in range(len(list(v_dict.values())[0]))]
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