In going over competing definitions of rights, we will frequently encounter arguments that seek to show that some thing is a necessary condition of having a right or that another thing is a sufficient condition of having a right.

For example, by definition, claim rights have corresponding duties.

That means that A’s having a claim right is a *sufficient condition* of B’s having a corresponding duty.

Conversely, B’s having a duty is a *necessary condition* of A’s having a claim right: if B does not have a corresponding duty, then A does not have a claim right.

So one way of showing that A does not have a claim right against B is to show that B does not have a corresponding duty: no corresponding duty, no claim right.

That wasn’t clear? Don’t worry. This page is devoted to explaining the underlying ideas.

## Sufficient conditions

If A is a sufficient condition of B, then you cannot have A without B.

For example, suppose that:

- A = receiving more than 50% of the votes
- B = winning the election

“Receiving more than 50% of the votes is a sufficient condition of winning the election” = the candidate who receives more than 50% of the votes wins the election.

So Kerry can claim to have won the election by virtue of meeting the sufficient condition for having won: receiving more than 50% of the votes.

Aside: those who follow elections in the US know that what counts is receiving the most votes in the Electoral College. Al Gore got the most individual votes last time, but he did not win the election because George Bush received more votes in the Electoral College.

## Necessary conditions

If C is a necessary condition of D, then you cannot have D without C.

For example, suppose that:

- C = receiving some votes
- D = winning the election

“Receiving some votes is a necessary condition of winning the election” = no one can win the election without receiving some votes.

If Kerry claims to have won the election, Bush can refute his claim by showing that the necessary condition was not met. That is, if he can show that Kerry did not receive some votes, he would show that Kerry did not win the election.

Note: you can meet the necessary condition without meeting the sufficient condition. Both candidates will receive some votes this year (the necessary condition), but only one will receive the most votes (the sufficient condition). Only the one that meets the necessary *and* sufficient conditions will win the election.

## Back and forth

You can reverse things in the following way: the second part is the *other* condition of the first part. Thus,

- A is a sufficient condition of B =

B is a necessary condition of A - C is a necessary condition of D =

D is a sufficient condition of C

### 1. Sufficient to necessary conditions

Suppose we grant that receiving more than 50% of the votes is a sufficient condition of winning the election. And suppose we also grant that Kerry did not win the election. It follows that Kerry did not receive more than 50% of the votes: if he had received more than 50% of the votes, he would have won the election but we have granted that did not happen.

This means that B (in this case “winning the election”) is a necessary condition of A (receiving more than 50% of the votes): you cannot have A without B or, you cannot receive more than 50% of the votes without winning the election.

### 2. Necessary to sufficient conditions

Conversely, winning the election is a sufficient condition of receiving some votes. If we grant that receiving some votes is a necessary condition of winning the election and that Bush won the election, it follows that Bush received some votes.

That means that D is a sufficient condition of C. You cannot win the election without receiving some votes.

### So these aren’t causes then, right?

Right. Winning the election is a sufficient condition of receiving some votes. But winning the election isn’t what causes a candidate to receive votes.

In general, it’s tempting to think about necessary and sufficient conditions in terms of causes and effects but that temptation should be resisted.

### Be careful

Someone can win the election without receiving more than 50% of the votes. There were three candidates running in the last Presidential election: Bush, Kerry, and Nader. The winner was the one who received *more* votes than the other two *even if that is less than 50%* of the votes.

In other words, A (receiving more than 50% of the votes) is a sufficient, but not a necessary, condition of B (winning the election).

Similarly, D (winning the election) is a sufficient, but not a necessary, condition of C (receiving some votes). You can receive some votes (C) without winning the election (D), therefore, winning the election (D) cannot be a necessary condition of receiving some votes (C).

## Definitions

What does this have to do with rights?

We are looking at definitions that put two things together, such as:

- claim rights and corresponding duties (the definition of a claim right)
- rights and having control over another person’s freedom (choice theories)
- rights and being the beneficiary of another person’s duties (benefit or interest theories)

In all of these cases, the two items are claimed to be necessary and sufficient conditions of one another.

You can dispute the definitions by showing that some widely accepted rights do not fit it, in the manner described above.

Qualification: sometimes, these definitions are simply stipulated. That’s what a claim right is, for example and, if that definition does not fit any known rights, that would just show that no known rights are claim rights, so defined.

In the other cases (choice and benefit theories), the definitions are proposals or theories. When that is so, you can dispute the proposal or theory by showing it doesn’t fit a significant portion of the rights that are commonly acknowledged.