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+A113: pick_first: Weighted Random Shuffling
+----
+* Author(s): Alex Polcyn (@apolcyn)
+* Approver: Mark Roth (@markdroth), Eric Anderson (@ejona86), Doug Fawley (@dfawley), Easwar Swaminathan (@easwars)
+* Status: In Review
+* Implemented in: <language, ...>
+* Last updated: Jan 26, 2026
+* Discussion at: https://groups.google.com/g/grpc-io/c/iCsweGDmUU4
+
+## Abstract
+
+Support weighted random shuffling in the pick first LB policy.
+
+## Background
+
+The pick first LB policy currently supports random shuffling. A primary intention of the feature
+is for load balancing, however it does not take (possibly present) locality or endpoint weights
+into account. Naturally this can lead to skewed load distribution and hotspots, when the load
+balancing control plane delivers varied weights and expects them to be followed.
+
+
+### Related Proposals: 
+* [A62](https://github.com/grpc/proposal/blob/master/A62-pick-first.md): pick_first: sticky TRANSIENT_FAILURE and address order randomization
+* [A42](https://github.com/grpc/proposal/blob/master/A42-xds-ring-hash-lb-policy.md) xDS Ring Hash LB Policy
+
+## Proposal
+
+### Changes within Pick First
+
+Modify behavior of pick_first when the `shuffle_address_list` option is set, and
+perform a weighted random sort *based on per-endpoint weights*. To do this, we will
+use the [Weighted Random Sampling](https://utopia.duth.gr/~pefraimi/research/data/2007EncOfAlg.pdf) algorithm
+proposed by Efraimidis, Spirakis:
+
+1) Assign a key to each endpoint, `u ^ (1 / weight)`, where `u` is a uniform random number in `(0, 1)` and weight
+is the weight of the endpoint (as present in a weight attribute). Default `weight` to 1 if no weight attribute is
+present.
+
+2) Sort endpoints by key in *descending* order.
+
+Note: the paper suggests `u` be in `(0, 1)` *exclusive*. Random numbers *on* zero or one effectively
+drop their weight. Also, technically zero will not transform to the exponential distribution that we are trying
+to create. However, load balancing skew introduced by such edge cases is unlikely to be noticeable, and so
+implementations are free to include these bounds so long as it does not cause other problems
+(e.g. crashes).
+
+
+### CDS LB Policy changes: Computing Endpoint Weights
+
+In XDS, we have a notion of both locality and endpoint weights. The expectation of the load balancing
+control plane is to *first* pick locality and *second* pick endpoint. The total probability distribution
+reflected by per-endpoint weights must reflect this. As such, we need to normalize locality weights within
+each priority and endpoint weights within locality; the final weight provided to `pick_first` should be a
+product of the two normalized weights (i.e. a logical AND of the two selection events).
+
+The CDS LB policy currently calculates per-endpoint weight attributes. It will continue to do so however
+we need to fix the mechanics: an endpoint's final weight should be a product of its *normalized* locality
+weight and *normalized* endpoint weight, rather than their product outright.
+
+Note: as a side effect this will fix per-endpoint weights in Ring Hash LB, which
+[currently](https://github.com/grpc/proposal/blob/master/A42-xds-ring-hash-lb-policy.md#change-child-policy-config-generation-in-xds_cluster_resolver-policy) are a product of the initial *raw* locality and endpoint weights.
+This "fix" will not require any changes within Ring Hash LB itself.
+
+We can continue to represent weights as integers if we represent their normalized values in
+fixed point UQ1.31 format. Math as follows (citation due for @ejona):
+
+```
+// To normalize:
+uint32_t ONE = 1 << 31;
+uint32_t weight = (uint64_t) weight * ONE / weight_sum;
+
+// To multiply the weights for an endpoint:
+weight = ((uint64_t) locality_weight * weight) >> 31;
+if (weight == 0) weight = 1;
+```
+
+Note: currently we round down to zero (and then up if we hit zero).
+We *could* use more accurate rounding schemes. However, rounding down
+is simple and should provide enough precision for load balancing
+purposes. For example, we only round down to zero if the product of
+two normalized weight probabilities is less than `2 ^ -31`, this kind
+of error is unlikely to cause noticeable skew in load balancing.
+
+### Temporary environment variable protection
+
+CDS LB policy and Pick First LB policy behavior changes will be guarded by `GRPC_EXPERIMENTAL_PF_WEIGHTED_SHUFFLING`.
+
+This should be enabled by default, after testing.
+
+## Rationale
+
+CDS LB policy changes are needed to generate correct weight distributions, not only for Pick First but
+also for Ring Hash.
+
+Reasons for UQ1.31 fixed point integers:
+
+- Predictable and acceptable bounds on precision.
+- Allows us to continue representing weights as integers internally.
+- Avoids risk of overflow bugs by preserving the (XDS) property that the sum of all weights within
+  a "grouping" does not exceed max uint32. For example note how if we used UQ32, *after*
+  normalization and multiplication a subsequent summation of endpoint weights in a locality may
+  result in uint32 overflow due to contributions of rounding errors.
+
+## Implementation
+
+TBD
+