diff --git a/src/pip/_internal/resolution/resolvelib/provider.py b/src/pip/_internal/resolution/resolvelib/provider.py
index fb0dd85f112..6cfdabf2ce4 100644
--- a/src/pip/_internal/resolution/resolvelib/provider.py
+++ b/src/pip/_internal/resolution/resolvelib/provider.py
@@ -105,6 +105,36 @@ def __init__(
     def identify(self, requirement_or_candidate: Union[Requirement, Candidate]) -> str:
         return requirement_or_candidate.name
 
+    def narrow_requirement_selection(
+        self,
+        identifiers: Iterable[str],
+        resolutions: Mapping[str, Candidate],
+        candidates: Mapping[str, Iterator[Candidate]],
+        information: Mapping[str, Iterable["PreferenceInformation"]],
+        backtrack_causes: Sequence["PreferenceInformation"],
+    ) -> Iterable[str]:
+        for identifier in identifiers:
+            if identifier in self._user_requested:
+                self._known_depths[identifier] = 1.0
+                continue
+
+            if identifier not in information:
+                self._known_depths[identifier] = math.inf
+                continue
+
+            parents = [
+                parent for _, parent in information[identifier] if parent is not None
+            ]
+            if not parents:
+                self._known_depths[identifier] = math.inf
+                continue
+
+            self._known_depths[identifier] = (
+                min(self._known_depths[parent.name] for parent in parents) + 1.0
+            )
+
+        return identifiers
+
     def get_preference(
         self,
         identifier: str,
@@ -158,23 +188,8 @@ def get_preference(
         pinned = any(op[:2] == "==" for op in operators)
         unfree = bool(operators)
 
-        try:
-            requested_order: Union[int, float] = self._user_requested[identifier]
-        except KeyError:
-            requested_order = math.inf
-            if has_information:
-                parent_depths = (
-                    self._known_depths[parent.name] if parent is not None else 0.0
-                    for _, parent in information[identifier]
-                )
-                inferred_depth = min(d for d in parent_depths) + 1.0
-            else:
-                inferred_depth = math.inf
-        else:
-            inferred_depth = 1.0
-        self._known_depths[identifier] = inferred_depth
-
         requested_order = self._user_requested.get(identifier, math.inf)
+        inferred_depth = self._known_depths[identifier]
 
         # Requires-Python has only one candidate and the check is basically
         # free, so we always do it first to avoid needless work if it fails.
diff --git a/src/pip/_vendor/resolvelib/resolvers/resolution.py b/src/pip/_vendor/resolvelib/resolvers/resolution.py
index da3c66e2ab7..ce304845bcb 100644
--- a/src/pip/_vendor/resolvelib/resolvers/resolution.py
+++ b/src/pip/_vendor/resolvelib/resolvers/resolution.py
@@ -411,24 +411,21 @@ def resolve(self, requirements: Iterable[RT], max_rounds: int) -> State[RT, CT,
             # keep track of satisfied names to calculate diff after pinning
             satisfied_names = set(self.state.criteria.keys()) - set(unsatisfied_names)
 
-            if len(unsatisfied_names) > 1:
-                narrowed_unstatisfied_names = list(
-                    self._p.narrow_requirement_selection(
-                        identifiers=unsatisfied_names,
-                        resolutions=self.state.mapping,
-                        candidates=IteratorMapping(
-                            self.state.criteria,
-                            operator.attrgetter("candidates"),
-                        ),
-                        information=IteratorMapping(
-                            self.state.criteria,
-                            operator.attrgetter("information"),
-                        ),
-                        backtrack_causes=self.state.backtrack_causes,
-                    )
+            narrowed_unstatisfied_names = list(
+                self._p.narrow_requirement_selection(
+                    identifiers=unsatisfied_names,
+                    resolutions=self.state.mapping,
+                    candidates=IteratorMapping(
+                        self.state.criteria,
+                        operator.attrgetter("candidates"),
+                    ),
+                    information=IteratorMapping(
+                        self.state.criteria,
+                        operator.attrgetter("information"),
+                    ),
+                    backtrack_causes=self.state.backtrack_causes,
                 )
-            else:
-                narrowed_unstatisfied_names = unsatisfied_names
+            )
 
             # If there are no unsatisfied names use unsatisfied names
             if not narrowed_unstatisfied_names: