The 3 way match is the central control of accounts payable and it asks one question: are we being billed for what we ordered and what actually arrived. Three documents answer it. The purchase order says what was agreed. The goods receipt says what turned up. The invoice says what you are being asked to pay. When all three agree, the invoice can be paid with confidence.
What is compared, exactly
Supplier identity, item, quantity and unit price, ideally line by line rather than on document totals. Line level matters because a single ordered line often arrives in two deliveries and is invoiced separately, and comparing totals turns that entirely normal situation into an exception. Tax and freight are usually handled separately, since they appear on the invoice and rarely on the order.
What each document protects against
The order protects against paying a price nobody agreed. The receipt protects against paying for goods that never arrived, which is the single most valuable protection in the set. The invoice is the claim being tested. Remove the receipt and you have a two-way match, which is appropriate for services and inadequate for goods.
Why it fails in practice
Almost always because one of the three does not exist. No purchase order because somebody bought without one; no goods receipt because nobody recorded the delivery. Genuine disagreements on price and quantity are the minority of exceptions in most teams. That means the match is usually improved upstream rather than by better matching software.
Questions people ask about 3 way match
Is a 3 way match always necessary?
For goods it is the standard control. For services and anything without a physical delivery, a two-way match against the order plus a confirmation the work was done is the sensible equivalent.
What is tolerance?
The size of difference allowed before an exception is raised. Usually a percentage with an absolute cap, set as policy and reviewed against real exceptions rather than left at a default.
Who resolves a failed match?
By reason: price to purchasing, quantity or missing receipt to whoever takes deliveries, and anything else to a named owner. Routing by reason is what makes exceptions clear quickly.