What is Arrow’s Impossibility Theorem?

Arrow’s impossibility theorem is a social-choice paradox illustrating the flaws of ranked voting systems. It states that a clear order of preferences cannot be determined while adhering to mandatory principles of fair voting procedures. Arrow’s impossibility theorem, named after economist Kenneth J. Arrow, is also known as the general impossibility theorem.

Understanding Arrow’s Impossibility Theorem

Democracy depends on people’s voices being heard. For example, when it is time for a new government to be formed, an election is called, and people head to the polls to vote. Millions of voting slips are then counted to determine who is the most popular candidate and the next elected official.

According to Arrow’s impossibility theorem, in all cases where preferences are ranked, it is impossible to formulate a social ordering without violating one of the following conditions:

• Nondictatorship: The wishes of multiple voters should be taken into consideration.
• Pareto Efficiency: Unanimous individual preferences must be respected: If every voter prefers candidate A over candidate B, candidate A should win.
• Independence of Irrelevant Alternatives: If a choice is removed, then the others’ order should not change: If candidate A ranks ahead of candidate B, candidate A should still be ahead of candidate B, even if a third candidate, candidate C, is removed from participation. 
• Unrestricted Domain: Voting must account for all individual preferences.
• Social Ordering: Each individual should be able to order the choices in any way and indicate ties.

Arrow’s impossibility theorem, part of social choice theory, an economic theory that considers whether a society can be ordered in a way that reflects individual preferences, was lauded as a major breakthrough. It went on to be widely used for analyzing problems in welfare economics. 

Example of Arrow’s Impossibility Theorem

Let’s look at an example illustrating the type of problems highlighted by Arrow’s impossibility theorem. Consider the following example, where voters are asked to rank their preference of three projects that the country’s annual tax dollars could be used for: A; B; and C. This country has 99 voters who are each asked to rank the order, from best to worst, for which of the three projects should receive the annual funding.

• 33 votes A > B > C (1/3 prefer A over B and prefer B over C)
• 33 votes B > C > A (1/3 prefer B over C and prefer C over A)
• 33 votes C > A > B (1/3 prefer C over A and prefer A over B)

Therefore,

• 66 voters prefer A over B
• 66 voters prefer B over C
• 66 voters prefer C over A

So a two-thirds majority of voters prefer A over B and B over C and C over A—a paradoxical result based on the requirement to rank order the preferences of the  three alternatives.

Arrow’s theorem indicates that if the conditions cited above in this article i.e. Non-dictatorship, Pareto efficiency, independence of irrelevant alternatives, unrestricted domain, and social ordering are to be part of the decision making criteria then it is impossible to formulate a social ordering on a problem such as indicated above without violating one of the following conditions.

History of Arrow’s Impossibility Theorem

The theorem is named after economist Kenneth J. Arrow. Arrow, who had a long teaching career at Harvard University and Stanford University, introduced the theorem in his doctoral thesis and later popularized it in his 1951 book Social Choice and Individual Values. The original paper, titled A Difficulty in the Concept of Social Welfare, earned him the Nobel Memorial Prize in Economic Sciences in 1972.

Arrow’s research has also explored the social choice theory, endogenous growth theory, collective decision making, the economics of information, and the economics of racial discrimination, among other topics.

What Is an Adhesion Contract?

An adhesion contract is an agreement where one party has substantially more power than the other in setting the terms of the contract. For a contract of adhesion to exist, the offeror must supply a customer with standard terms and conditions that are identical to those offered to other customers. Those terms and conditions are non-negotiable, meaning the weaker party in the contract must agree to the contract as it is rather than requesting clauses be added, removed, or changed. Adhesion contracts may also be referred to as boilerplate contracts or standard contracts.

Understanding Adhesion Contracts

Adhesion contracts are often used for insurance, leases, vehicle purchases, mortgages, and other transactions where there will be a high volume of customers who will all fall under some standard form of agreement. In an insurance contract, the company and its agent have the power to draft the contract, while the potential policyholder only has the right of refusal; the customer cannot counter the offer or create a new contract to which the insurer can agree. It is important to read over an adhesion contract carefully, as all the information and rules have been written by the other party.

Adhesion contracts are usually enforceable in the United States thanks to the Uniform Commercial Code (UCC). The UCC helps to ensure that commercial transactions are taking place under a similar set of laws across the country. Although the UCC is followed by most American states, it has not been fully adopted by some jurisdictions like American Samoa and Puerto Rico. Louisiana stands alone among the 50 states in that it has only adopted parts of the UCC. The UCC has specific provisions relating to adhesion contracts for the sale or lease of goods. Contracts of adhesion are, however, subject additional scrutiny and interpretation under state law.

History of Adhesion Contracts

Adhesion contracts originated as a concept in French civil law, but did not enter American jurisprudence until the Harvard Law Review published an influential article on the subject by Edwin W. Patterson in 1919. Subsequently, most American courts adopted the concept, helped in large part by a Supreme Court of California case that endorsed adhesion analysis in 1962. 

As with most aspects of contract law, the legality and enforceability of adhesion contracts has been formed over time. The case law and interpretation may vary from state to state, but it is generally agreed that adhesion contracts are an efficient way to handle standardized transactions. Using adhesion contracts saves companies and customers time and money in terms of legal counsel when they are done properly. However, the law around adhesion contracts is always evolving. For example, digital adhesion contracts signed online have been challenged in court for burying clauses or making it difficult to read certain clauses, so a digital adhesion contract must now be as close to a paper contract as possible.

Enforceability of Adhesion Contracts

For a contract to be treated as an adhesion contract, it must be presented as a “take it or leave it” deal, giving one party no ability to negotiate because of their unequal bargaining position. Adhesion contracts are subject to scrutiny, though, and that scrutiny usually comes in one of two forms.

Courts have traditionally used the doctrine of reasonable expectations to test whether an adhesion contract is enforceable. Under this doctrine, specific parts of an adhesion contract or the whole contract may be deemed unenforceable if the contract terms go beyond what the weaker party would have reasonably expected. Whether a contract is reasonable in its expectations depends on the prominence of the terms, the purpose of the terms, and the circumstances surrounding acceptance of the contract.

The doctrine of unconscionability has also been used in contract law to challenge certain adhesion contracts. Unconscionability is a fact-specific doctrine arising from the same equitable principles—specifically the idea of bargaining in good faith. Unconscionability in adhesion contracts usually comes up if there is an absence of meaningful choice on the part of one party due to one-sided contract provisions combined with unreasonably oppressive terms that no one would or should accept. Simply put, if the contract is exceptionally unfair to the signing party, it can be declared unenforceable in court.

The doctrine of unconscionability shifts the focus from what the customer might reasonably expect to the motive of the supplier. Unconscionability is easier to argue if the supplier is making a significant profit from the agreement, especially if the amount of profit is in some way tied to the weaker party’s lack of bargaining power. Some legal experts have pushed back on this approach as it has implications in terms of the freedom of contract—the legal concept that people can freely determine the provisions of a contract without government interference.

What Are China A-Shares?

China A-shares are the stock shares of mainland China-based companies that trade on the two Chinese stock exchanges, the Shanghai Stock Exchange (SSE) and the Shenzhen Stock Exchange (SZSE). Historically, China A-shares were only available for purchase by mainland citizens due to China’s restrictions on foreign investment.

However, since 2003, select foreign institutions have been able to purchase these shares through the Qualified Foreign Institutional Investor (QFII) system. Established in 2002, the QFII program allows specified licensed international investors to buy and sell on mainland China’s stock exchanges.

A-shares are also known as domestic shares because they use the Chinese renminbi (RMB) for valuation.

China A-Shares vs. B-Shares

China A-shares are different from B-shares. A-shares are only quoted in RMB, while B-shares are quoted in foreign currencies, such as the U.S. dollar, and are more widely available to foreign investors. Foreign investors may have difficulty accessing A-shares because of Chinese government regulations, and Chinese investors may have difficulty accessing B shares most notably for currency-exchange reasons. Some companies opt to have their stock listed on both the A-shares and B-shares market.

Due to the limited access of Chinese investors to B-shares, the stock of the same company often trades at much higher valuations on the A-shares market than on the B-shares market. Although foreign investors may now invest in A-shares, there is a monthly 20% limit on repatriation of funds to foreign countries.

The Shanghai Stock Exchange (SSE) publishes the key performance index for A-shares, known as the SSE 180 Index. In composing the index, the exchange selects 180 stocks listed on the SSE. The selection is diversified between sector, size, and liquidity to ensure adequate representation. Thus, the index’s performance benchmark reflects the overall situation and operation of the Shanghai securities market.

History of China A-Shares

Since its inception in 1990, including a major reform in 2002, the index has seen great fluctuations. However, it has grown along with the Chinese economy. The years 2015 to 2016 were a particularly difficult period, with a 52-week performance of -21.55% as of July 20, 2016.

As China grows from an emerging market to an advanced economy, there is substantial demand for Chinese equity. Stock exchange regulators continue efforts to make A-shares more broadly available to foreign investors and have them recognized by the global investing community.

In June 2017, the MSCI Emerging Markets Index announced a two-phase plan in which it would gradually add 222 China A large-cap stocks. In May 2018, the index began to partially include China large-cap A shares, which make up 5% of the index. Full inclusion would make up 40% of the index.

It is important for countries such as China to open their markets to global investors to stay competitive and thrive economically. China A-shares provide an alternative investment for those interested in trading in Chinese securities.

What Is a 125% Loan?

A 125% loan is a type of leveraged loan, typically a mortgage used to refinance a home, which allows a homeowner to borrow an amount equal to 125% of their property’s appraised value.

For example, if a home is worth $300,000, then a 125% loan would give the borrower access to $375,000 in funds.

How a 125% Loan Works

In financing terminology, a 125% loan has a loan-to-value (LTV) ratio of 125%. The LTV ratio, which compares the size of a loan relative to the appraised value of the property that serves as security, is used by lenders to judge a loan’s default risk. A 125% loan is considered riskier than one with an LTV ratio of less than 100%. In fact, with conventional mortgages, the loan size does not typically exceed 80% of a property’s value.

Therefore, according to the risk-based pricing method used by lenders, a loan with an LTV ratio of 125% will carry a higher interest rate than one with a lower LTV ratio—as much as double, in some instances.

Using a 125% Loan for Refinancing

Homeowners who take out a 125% loan usually do so when refinancing their homes to gain access to more cash than they would have available from their home equity. Their motive might be to use the loan to pay off other debts that carry even higher interest rates, such as credit cards.

But because 125% loans have high interest rates and may also have additional fees, anyone who is considering one should plan to shop around for the best terms they can get.

If your goal is to obtain cash to pay off other debt, and you are unable to qualify for a 125% loan (or you decide that you simply don’t want one), then you might still consider a home equity loan. You won’t get as much cash out of it, but the interest rate is likely to be considerably lower, and you can use it to pay off at least a portion of your high-interest debt. Another option would be to do a cash-out refinance.

Advantages and Disadvantages of 125% Loans

The advantage of a 125% loan is that it can allow a homeowner, especially one who has not accumulated too much home equity or whose property has actually declined in value, to obtain more cash than they otherwise could.

The disadvantage—to borrower and lender alike—is the added risk compared with a smaller loan. The borrower will be on the hook for more debt, and the lender will face added risk in case of a default. If the borrower does default, the lender can foreclose on the property and sell it, but the lender is very unlikely to get all of its money back.

History of 125% Loans

The 125% loans first became popular during the 1990s, in some cases geared toward low-risk borrowers with high credit scores who wanted to borrow more than their available home equity. Along with other factors, 125% loans played a role in the 2007–08 housing crisis. The crash of real estate markets around the country, kicked off by the subprime mortgage meltdown, left many people “underwater”—that is, they owed more money on their mortgage than their home was actually worth.

As home values dropped, some homeowners who wanted to refinance found that they no longer had enough equity in their homes to qualify for a new loan. Moreover, they could not recoup their losses even if they managed to sell the home.

The now-expired federal Home Affordable Refinance Program (HARP) was introduced in March 2009 as a way to offer relief. It allowed homeowners whose homes were underwater, but who were otherwise in good standing and current with their mortgages, to apply for refinancing. Through HARP, homeowners who owed up to 125% of the value of their homes could refinance at lower rates to help them pay off their debts and get on sounder financial footing.

Originally, homeowners who owed more than that percentage could not apply. But eventually, even the 125% LTV ceiling was removed, allowing still more homeowners to apply for HARP loans. After being extended several times, HARP ended in December 2018.