Last writer wins: a deterministic choice with a clock problem

Model a register state as a value paired with a totally ordered tag. Merge returns the pair with the greatest tag, using a stable tie-breaker when timestamps agree. The tie-breaker must distinguish otherwise competing writes or prescribe the same final value everywhere; merely choosing whichever message arrived last is not deterministic across replicas. A common illustrative tag is (timestamp,actor-ID), but multiple writes by one actor at one timestamp require an additional counter or another uniqueness discipline.

This maximum operation is associative, commutative, and idempotent when tags form a valid total order and identical tags cannot represent conflicting payloads. These properties explain convergence under repeated and reordered state exchange. They do not prove that the greatest timestamp is the latest real event, nor that losing a value is appropriate. A convergent color preference and a convergent audit log have very different requirements. Write down whether discarded alternatives remain available for recovery or disappear permanently.

Let a local physical reading equal real time plus an offset. If two offsets differ by more than the elapsed real time between writes, their timestamp order can reverse. A clock jumping backward can also make a writer’s new timestamp smaller than one it previously emitted. A badly fast clock may dominate updates from otherwise healthy replicas until they catch up. Timestamp validation and monotonic local generation can limit some damage, but each additional rule must be part of the documented protocol.

Logical clocks can respect a happens-before relation when their update and message rules are followed, while still assigning arbitrary order to concurrent events. Hybrid logical clocks combine physical-time information with logical components to preserve causal ordering under their stated algorithm; they do not eliminate uncertainty about real-time order of concurrent edits. None of these tags by itself supplies multi-object transactions, uniqueness constraints, or an inventory floor. Distinguish the mathematical convergence proof from whatever physical-time or business interpretation a product places on the winner.

For a display preference, choosing one concurrent update may be an acceptable documented policy. For an address change, retaining alternatives and asking the user can be safer. For an immutable audit event, store both events rather than treating an overwritten register as a history. Applications should expose conflict indicators when needed and test clock offsets, equal timestamps, delayed delivery, and repeated updates from a single actor. Authorized clients also need a controlled tag-generation policy if arbitrary timestamps could suppress other writers.

The modular lab illustrates why a finite wrapping tag alone cannot represent unlimited recency. Reset, set modulus m=8 and additive step a=1, predict the current residue zero, then Step repeatedly. After eight transitions the residue returns to zero. This is not a wall clock or an LWW register: its only model is addition modulo m. The useful counterexample is that repeating labels cannot by themselves distinguish an old event from a new one. Real clock tags need their own ordering and reuse rules.