The Paradoxical Optimal Voting Strategy for the Presidential Election of 2016

Most people agree that when you vote in an election, to maximize your utility, the best voting strategy is to vote for your better preferred candidate of the two most popular candidates assuming  simple plurality is used. This was not the case in 2016’s US presidential election. Both major candidates were deemed so incapable that they could be defeated by any typical candidate in the opposing party. As a result, expecting that the winner will run for reelection and lose in 2020, the best strategy becomes voting for the party you like the least, as the current short loss would trade for a longer victory in the future. This assumes that Trump and Hillary each represent their party well and attract voters who usually vote for their party. We also assume a zero discount rate: a miserable 4 years that starts in 4 years weighs equally as a miserable 4 years that starts immediately.

Created by Christopher Wang. First published on November 8, 2016 on

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9 Chrome Extensions for Surfing the Web Statistically

There are a lot of data on the web that can help us surf the internet more efficiently. The extensions listed below help us achieve this. Some extensions collect data from the users and summarize them, some analyze user-generated content, while others record the history of web pages. SEO oriented extensions are excluded from this list.

1. Alexa Traffic Rank


This extension shows the global website traffic ranking of the current website as well as the ranking in the country that generates the most traffic for this website. This is the quickest way to learn about a website’s popularity and credibility. Moreover, it shows websites that are similar to the current one with remarkable validity. This enables a graph based traversal of the internet. The Wayback Machine link allows the user to view old versions of the main page of the current website. To view old versions of any web page, there is a dedicated extension listed below at #9.

Upon clicking on the main link, it shows the traffic distribution overtime, by country, subdomain, gender, education, and browsing location. Traffic data is collected mainly through the Alexa Toolbar and this extension.

Number of users: 550,000

Alternatives: SimilarWeb with better graphics but less reliable traffic rankings.

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Welfare Economics of Labor Migration


Should the United States allow immigrants and to what extent? This is a topic of hot debate because both the economics behind it is unintuitive and everybody’s goal or preference is different.

Are low skill immigrants taking our jobs away?

This is only true for a small portion of the population, the unskilled citizens, or citizens worse skilled than the average low skill immigrants. When low skill immigrants come, the wage in low skill occupations decreases as the labor supply increases (proportionally more than the increase in the size of the economy). Low skill citizens suffer and employers (the producer) benefit from a lower cost of labor. From standard welfare analysis, we know the gain for the producers is definitely greater than the loss of the low skill citizens, resulting in a higher social welfare.

Assume that our country has an excess of higher skill labors, meaning some skilled workers accepted a lower skill job because the high skill job market is saturated or because the low skill job’s salary is attractive. But wait, could a free market be saturated? Because for each high skill job, there has to exist some low skill job to complement it. For example, each company needs customer service (a low skill occupation). If few low skill workers are available, wage will increase, attracting some high skill workers. The customer service will still exist but rather small. This assumption of excess high skill labor is reflected in the high wage of low skill jobs that attracts immigrants.

After the influx of immigrants, many high skilled citizens in low skill occupations will switch to high skill jobs as the wage in low skill jobs decreases (relative to high skill jobs). High skill jobs of course mean higher productivity. When the citizens shift to a higher skilled worker makeup, the country’s GNP (only counting citizens) is bound to increase since the total productivity increases. This resonates with the increasing social surplus I mentioned earlier. A higher productivity benefits both producer and consumer, including low skilled citizens who are worker under a lower wage.

Conclusions: if we allow low skill immigrants

  1. Low skill citizens can be better off or worse off depending on the situation.
  2. High skill citizens are better off
  3. Citizens become richer, on average.

Continue reading “Welfare Economics of Labor Migration”

What does It Really Cost to Buy Any Tangible Goods?

What does it cost when you buy a 300-page paperback from Amazon? The price of the book is only the initial cost. When you store it on your bookshelf, it takes space and renting a space costs money. The price of the book might be only $10; the storage cost for 15 years is probably higher than $5.5.

A 1000 square feet apartment costs around $2100/month in the US. Roughly $300 of the cost is fixed cost independent of the size of usable area, including the cost of transaction, management cost, stairs, mechanical rooms, and partly the costs of outdoor areas, utility bills, and property tax. The rest of the rent should grow linearly with area. This leaves $1800/month for 1000 sq ft, or $1.8/month/sq ft, or $0.0125/month/sq inches.

In the short run, buying a book will not increase your rent, but in the long run you are mobile and you will pick a house that’s about the right size by equating your marginal benefit per sq ft per month to around $1.8.

Assume that a book is 8’’ × 5.5’’ × 1’’, and your bookshelf is 29’’ × 12’’ × 72’’ with 6 shelves plus the top. To calculate the minimal needed space, we squeeze as many bookshelves as possible in a library pattern, with aisles that are only 24’’ wide. Half of the area will be bookshelves and half will be aisles since 2 × bookshelf depth = aisle width. A book would cost 1’’ (width) × 12’’ (depth) of space on one of seven shelves (including the top) and an equal share of aisle space. Therefore, one book occupies 1” × 12” ÷ 7 shelves × 2 = 3.42 square inches of space.

Now the cost of storing one book a month is 0.0125 × 3.42 = $0.04286; or $0.5143 a year. Fifteen years? Let’s use a realistic annual discount rate of 4.5% to calculate the present value: $0.5143 / 0.045 × (1 – 1 / 0.045^15) = $ 5.5232. To store a book forever, the cost is: $0.5143 / 0.045 = $11.4286. Next time you bring home a free book from library, beware that you are signing a contract to pay 51 cents each year (adjust for inflation) until you get rid of the book.

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