Voting Methods/Reapportionment
What does Volić argue the best voting method is? Why? (Do you know the 5 methods to voting?)
According to Volić, instant runoff is the best method because there is evidence that it works, it works against spoilers, helps elect more women and people of color, and is easy to use. (5 methods are Borda count, instant runoff, runoff, Copeland's method, and plurality)
What is packing and what is cracking in gerrymandered districts? Can a spreadsheet help prevent/detect/fix this?
Packing: fills one or more districts with voters of one party. Cracking: splitting majority so they count less
Sample answer: A spreadsheet can help analyze past election data and create predicted outcomes without packing/cracking districts to see unbiased results. You can then compare the difference between the spreadsheet election and the actual election to see if there are forms of gerrymandering.
What are the definitions of Present Value and Net Present Value?
Present value is the current value of a future sum of money based on a constant rate of return. Net present value is how much an investment is worth throughout its lifetime, discounted to today's value. NPV is higher if payments are paid earlier.
What are shift ciphers? What are Vigenère ciphers? Compare and contrast.
Shift ciphers are when you pick a number between 0-25 and shift every letter in a message by N (forward).
Vigenère ciphers is when you pick a word, shift the letters in a message by the letters in the keyword periodically.
Bonus question! How might a spreadsheet or algorithm be used to analyze the kinds of urban changes Alexis Madrigal spoke about in his lecture, that is described in his book, The Pacific Circuit?
By organizing and analyzing data, such as housing prices, eviction rates, or demographic shifts a spreadsheet can show how global capital flows and impacts specific neighborhoods in cities like San Francisco.
How do modified divisors work in apportionment methods, and which specific voting methods use them?
A modified divisor is a divisor that's adjusted from the standard divisor (total population/size of the house) until the quotas equals the number of seats, all of which can be accomplished in a spreadsheet. A modified divisor is used in Jefferson’s Method, Adam’s Method, and Huntington-Hill Method.
How does Benjamin define the "New Jim Code"? How does Benjamin argue that technology and algorithms are subjective, what example does she use to support this claim?
A set of technologies that reinforce and reproduce racial discrimination, but are seen as progressive and better than the previous systems of discrimination. This racial code aims to promote social control.
Benjamin argues that technology is subjective because it is designed and created by humans who have their own biases which are then added into the algorithm. As a result, an algorithm can also make judgements or interpretations. She uses the example of California’s gang database.
What is the equation for simple interest? What is the equation for compound interest? (principle=P, interest=r, years=t)
Simple interest: F = P(1 + tr)
How are spreadsheets key players in deciphering codes? Do you believe that they are important tools in making and breaking codes?
Sample answer: Spreadsheets are convenient and easy to use. Instead of decrypting codes by hand, you are able to solve and figure out a message in minutes. I believe that spreadsheets are vital tools when it comes to cryptography, as there is no bias or judgements.
What are the benefits that having a spreadsheet which can calculate “self-amortizing mortgages”? How can this help people who might not know much about mortgages?
Sample answer: Self-amortizing mortgages involve payments over a set term that cover both interest and the loan. A spreadsheet can automatically break down the monthly payments which makes it easy to see how much of each payment goes toward interest vs. reducing the loan. Additionally, being able to alter the spreadsheet by inputting their own loan amount allows one to get personal results. Spreadsheets also help organize the information in a clear, coherent, understandable way for people who might not have much experience with loans.
In what ways can spreadsheets be used to analyze alternative voting systems like ranked choice voting (instant runoff voting), as suggested by Volić?
Spreadsheets can be used to replicate ranked choice voting by sorting voter preferences in rows and automatically eliminating the lowest-ranked candidates through formulas. (Volić explains how tools like this can make it easier for individuals to understand how different voting systems affect outcomes and representation.)
In what ways does Volić propose using mathematics and tools like spreadsheets, to detect and prevent gerrymandering?
Volić proposes using math and spreadsheets to fight against gerrymandering by creating many random, fair maps and comparing them to the proposed map in order to identify potential biases. Using the efficiency gap to measure the fairness can also be calculated in a spreadsheet.
How do you calculate NPV on a spreadsheet? Why is this important?
Google sheets has a function where you type “NPV” and it will calculate it for you. The equation is =NPV(discount, cashflow1, [cashflow2, …]). This is important because it considers the time value of money, which helps people make informed decisions if one should pursue an investment, as it can tell if the investment is potentially profitable.
In “Recognizable Without Being Known”, Brunton explains what an asymmetrical arrangement is. What is it and what would someone sending an encrypted message send (what letters)?
Asymmetrical is when there is a private key and public key in which you can share your public key without jeopardizing the security of your message. So say you encrypt a message with someone’s public key, only their private key can decrypt it.
How can a spreadsheet be used to evaluate the potential impact of the Congestion Relief Plan on both New York City residents and visitors? Additionally, how can a spreadsheet be used to predict the MTA's revenue over a certain number of years based on congestion pricing data?
Sample answer: A spreadsheet can support both the MTA and New York City residents and visitors by analyzing whether the Congestion Relief Plan is likely to create meaningful change. By inputting data from the previous few months, a spreadsheet can help identify patterns and create possible outcomes that is based on current trends. This allows for predictions from real data about traffic flow, commuter behavior, and potential revenue.
How can spreadsheets be used to replicate the Hamilton Method of apportionment (summarize what needs to be in the spreadsheet, not the codes because that might take too long!)? Can this spreadsheet help us understand paradoxes such as the Alabama paradox or the New States paradox?
Briefly, by organizing a spreadsheet so there is a column for states, population of the states, quota, rounding down, remainders, and a cell for total population, seats in parliament, seats allocated and seats remaining you will have the basics for creating a spreadsheet to simulate the Hamilton Method (although you would still need to code the cells, such as for the quota column you would need to take the state population, divide by total population and multiply it by the number of seats in parliament.)
Yes you are able to clearly see the Alabama paradox because it can show you when you increase the number of seats, you will see what state loses a seat. And also you can see the New States paradox because if you add a new state, you will be able to see the reapportionment, and if another state loses a seat.
How might using algorithms and spreadsheets in redistricting or gerrymandering reinforce the dangers O’Neils terms as “Weapons of Math Destruction”? Are there any ethical concerns that arise if we were to implement these tools in elections?
Sample answer: Many weapons of math destruction (WMD) are designed to be opaque and intimidating. Most WMDs are not transparent for the average person to know and understand what is going on. Gerrymandering shows how the same mathematical tools that can be used for good can also be weaponized, especially when they are not investigated and made to serve the powerful.
How did Deringer explain that calculations like present value (PV) and net present value (NPV) began shaping people’s understanding of time?
NPV and PV changed people's perceptions about time and money, especially when thinking about the future. They began to calculate if investment would be worth it and so Deringer argues that it helped people make better decisions about loans, investments, and debts.
Can you provide the 3 steps of deciphering a shift cipher with RSA?
Factor (N) → p and q.
(1+whole number*(p-1)(q-1))/e → D
(C^d) mod N → M
Based on Francis Su’s work, why do you believe people are so removed from mathematics? How can we be so reliant on something we might not fully understand?
Sample answer: I believe that people are so removed because many don't understand the profound impact that mathematics has on people, our society, our daily lives. We don’t always explicitly see it, like how we might be able to see the impact that science has with new discoveries and such. Math is embedded in every institution, whether we see it or not. And it is that reason that we are so reliant on it, because it is in our everyday lives and we depend on it.