science

Symmetry (social choice)

Symmetry (social choice) is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Symmetry (social choice) rather than just read about it. In short: In economics and social choice, a function satisfies symmetry, neutrality, or anonymity if the rule does not discriminate between different participants ahead of time. For example, in an election, a voter-anonymous function is one where it does not matter who casts which vote, i.e. all voters' ballots are equal ahead of time.

Key takeaways

Symmetry (social choice) belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Symmetry (social choice) to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Symmetry (social choice) from memory before moving on to harder problems.

Reference excerpt

In economics and social choice, a function satisfies symmetry, neutrality, or anonymity if the rule does not discriminate between different participants ahead of time. For example, in an election, a voter-anonymous function is one where it does not matter who casts which vote, i.e. all voters' ballots are equal ahead of time. Formally, this is defined by saying the rule returns the same outcome (whatever this may be) if the votes are "relabeled" arbitrarily, e.g. by swapping votes #1 and #2. Similarly, outcome-neutrality says the rule does not discriminate between different outcomes (e.g. candidates) ahead of time. Formally, if the labels assigned to each outcome are permuted arbitrarily, the returned result is permuted in the same way. Some authors reserve the term anonymity for agent symmetry and neutrality for outcome-symmetry, but this pattern is not perfectly consistent.

Examples Most voting rules are anonymous and neutral by design. For example, plurality voting is anonymous and neutral, since only counts the number of first-preferences for each candidate, regardless of who cast these votes. Any rule that uses a secret ballot must be voter-anonymous, since they do not know which voter cast which vote. However, the converse is not true (as in e.g. roll call votes).

Non-examples An example of a non-neutral rule is a rule which says that, in case of a tie, the alternative X is selected. This is particularly prominent in cases where X is the status quo option: parliamentary procedures often specify that the status quo unless there is a strict majority against it. Other rules are non-anonymous in the case of a tied vote, e.g. when a chairman is allowed to break ties. However, not all violations of anonymity and neutrality are due to tied votes. For example, many motions require a supermajority to pass, and other rules can give certain stakeholders a veto. The United States' electoral college is a well-known example of a non-anonymous voting rule, as the results of the election depend not just on the votes for each candidate, but also on their physical arrangement across space. Weighted voting rules are non-anonymous, as they give some voters a higher weight than others, for example, due to their expertise or entitlement.

See also One man, one vote Fair election

References

Worked examples

Example 1 — a first encounter with Symmetry (social choice)

Start with the simplest possible case. Write down what Symmetry (social choice) claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Symmetry (social choice) before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Symmetry (social choice) ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Symmetry (social choice)

In research: Symmetry (social choice) appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Symmetry (social choice) in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Symmetry (social choice) is common in secondary-school and first-year university syllabi. It links to neighbouring topics Social choice theory, so understanding it makes those chapters shorter.
In everyday life: Look for Symmetry (social choice) outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Symmetry (social choice)” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Symmetry (social choice) in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Symmetry (social choice) means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Symmetry (social choice) out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Symmetry (social choice) in simple terms?

Why does Symmetry (social choice) matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Symmetry (social choice)?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Symmetry (social choice).