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 Audit Risk?

Audit risk is the risk that financial statements are materially incorrect, even though the audit opinion states that the financial reports are free of any material misstatements.

Understanding Audit Risk

The purpose of an audit is to reduce the audit risk to an appropriately low level through adequate testing and sufficient evidence. Because creditors, investors, and other stakeholders rely on the financial statements, audit risk may carry legal liability for a certified public accountancy (CPA) firm performing audit work.

Over the course of an audit, an auditor makes inquiries and performs tests on the general ledger and supporting documentation. If any errors are caught during the testing, the auditor requests that management propose correcting journal entries.

At the conclusion of an audit, after any corrections are posted, an auditor provides a written opinion as to whether the financial statements are free of material misstatement. Auditing firms carry malpractice insurance to manage audit risk and the potential legal liability.

Types of Audit Risk

The two components of audit risk are the risk of material misstatement and detection risk. Assume, for example, that a large sporting goods store needs an audit performed, and that a CPA firm is assessing the risk of auditing the store’s inventory.

Risk of Material Misstatement

Material misstatement risk is the risk that the financial reports are materially incorrect before the audit is performed. In this case, the word “material” refers to a dollar amount that is large enough to change the opinion of a financial statement reader, and the percentage or dollar amount is subjective. If the sporting goods store’s inventory balance of $1 million is incorrect by $100,000, a stakeholder reading the financial statements may consider that a material amount. The risk of material misstatement is even higher if there is believed to be insufficient internal controls, which is also a fraud risk.

Detection Risk

Detection risk is the risk that the auditor’s procedures do not detect a material misstatement. For example, an auditor needs to perform a physical count of inventory and compare the results to the accounting records. This work is performed to prove the existence of inventory. If the auditor’s test sample for the inventory count is insufficient to extrapolate out to the entire inventory, the detection risk is higher.

What Is All Risks?

“All risks” refers to a type of insurance coverage that automatically covers any risk that the contract does not explicitly omit. For example, if an “all risk” homeowner’s policy does not expressly exclude flood coverage, then the house will be covered in the event of flood damage.

This type of policy is found only in the property-casualty market.

Understanding All Risks

Insurance providers generally offer two types of property coverage for homeowners and businesses—named perils and “all risks.” A named perils insurance contract only covers the perils stipulated explicitly in the policy.

For example, an insurance contract might specify that any home loss caused by fire or vandalism will be covered. Therefore, an insured who experiences a loss or damage caused by a flood cannot file a claim to his or her insurance provider, as a flood is not named as a peril under the insurance coverage. Under a named perils policy, the burden of proof is on the insured.

An all risks insurance contract covers the insured from all perils, except the ones specifically excluded from the list. Contrary to a named perils contract, an all risks policy does not name the risks covered, but instead, names the risks not covered. In so doing, any peril not named in the exclusions list is automatically covered.

The most common types of perils excluded from “all risks” include earthquake, war, government seizure or destruction, wear and tear, infestation, pollution, nuclear hazard, and market loss. An individual or business who requires coverage for any excluded event under “all risks” may have the option to pay an additional premium, known as a rider or floater, to have the peril included in the contract.

Burden of Proof

The trigger for coverage under an “all risks” policy is physical loss or damage to property. An insured must prove physical damage or loss has occurred before the burden of proof shifts to the insurer, who then has to prove that an exclusion applies to the coverage.

For example, a small business that experienced a power outage may file a claim citing physical loss. The insurance company, on the other hand, might reject the claim stating that the company experienced a loss of income from a mere loss of property use, which is not the same thing as a physical loss of property.

Special Considerations

Because “all risks” is the most comprehensive type of coverage available and protects the insured from a greater number of possible loss events, it is priced proportionately higher than other types of policies. The cost of this type of insurance should, therefore, be measured against the probability of a claim.

It is possible to have named perils and “all risks” in the same policy. For example, an insured may have a property insurance policy that has all risks coverage on the building and named perils on his personal property. Everyone should read the fine print of any insurance agreement to ensure that they understand what is excluded in the policy.

Also, just because an insurance policy is termed “all risks” does not mean that it covers “all risks” since the exclusions reduce the level of coverage that is offered. Make sure you look for the exclusions in any prospective policy.

The Bottom Line

All risk insurance, also called all risk coverage, is an insurance product that covers any incident that isn’t explicitly mentioned. These policies assume a good deal of risk for the insurer and are less common than named risk coverage, which states exactly what is covered, versus stating only what is to be omitted (which is the case with all risk).

What Are Administrative Expenses?

Administrative expenses are expenses an organization incurs that are not directly tied to a specific core function such as manufacturing, production, or sales. These overhead expenses are related to the organization as a whole, as opposed to individual departments or business units.

Understanding Administrative Expenses

Administrative expenses may include salaries of senior management and the costs associated with general services or supplies; for example, legal, accounting, clerical work, and information technology. These costs tend not to be directly related to the production of goods or services of a business and are usually excluded from gross margins.

Companies incur administrative expenses in order to perform basic operations (e.g., administer payroll or healthcare benefits), increase oversight and efficiency, and/or comply with laws and regulations. On the income statement, administrative expenses appear below cost of goods sold (COGS) and may be shown as an aggregate with other expenses such as general or selling expenses.

Some administrative expenses are fixed in nature, as they are incurred as part of the foundation of business operations. These expenses would exist regardless of the level of production or sales that occur. Other administrative expenses are semi-variable. For example, a business will always use some minimum level of electricity to keep the lights on. Beyond that point, it can take measures to reduce its electric bill.

Because a business can eliminate administrative expenses without a direct impact on the product it sells or produces, these costs are typically first in line for budget cuts. Management is strongly motivated to maintain low administrative expenses relative to other costs, as this allows a business to utilize leverage more effectively. The sales-to-administrative expense ratio helps companies to measure how much sales revenue is being portioned to covering administrative costs.

Companies can deduct from their tax returns administrative expenses that are reasonable, ordinary, and necessary for business operations. These expenses must be incurred during the usual course of business and deducted in the year they are incurred.

Other Types of Administrative Expenses

Wages and benefits to certain employees, such as accounting and IT staff, are considered administrative expenses. All executive compensation and benefits are considered an administrative expense. Building leases, insurance, subscriptions, utilities, and office supplies may be classified as a general expense or administrative expense.

Depending on the asset being depreciated, depreciation expenses may be classified as a general, administrative, or selling (marketing) expense. Organizations may choose to include consulting and legal fees as an administrative expense as well. However, research and development (R&D) costs are not considered administrative expenses.

To get the full picture of the costs associated with running certain business units, a company may allocate out administrative expenses to each of its departments based on a percentage of revenue, expenses, square footage, or other measures. Internally, this allows management to make decisions about expanding or reducing individual business units.

Example of Administrative Expenses

For example, if XYZ Company spends $4,000 monthly on electricity and records this as an administrative expense, it might allocate the cost according to the square footage each individual department occupies. Assume:

• The production facility is 2,000 square feet
• The manufacturing facility is 1,500 square feet
• The accounting office is 750 square feet
• The sales office is 750 square feet

The company occupies 5,000 square feet. The electric bill could be allocated as follows:

• Production: $1,600 or (2,000 / 5,000) x $4,000
• Manufacturing: $1,200 or (1,500 / 5,000) x $4,000
• Accounting: $600 or (750 / 5,000) x $4,000
• Sales: $600 or (750 / 5,000) x $4,000