diff --git a/narwhals/_arrow/expr.py b/narwhals/_arrow/expr.py
index 2cae743f83..1cb0a068cb 100644
--- a/narwhals/_arrow/expr.py
+++ b/narwhals/_arrow/expr.py
@@ -151,55 +151,64 @@ def __and__(self: Self, other: ArrowExpr | bool | Any) -> Self:
         return reuse_series_implementation(self, "__and__", other=other)
 
     def __rand__(self: Self, other: ArrowExpr | bool | Any) -> Self:
-        return reuse_series_implementation(self, "__rand__", other=other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__and__(self)  # type: ignore[return-value]
 
     def __or__(self: Self, other: ArrowExpr | bool | Any) -> Self:
         return reuse_series_implementation(self, "__or__", other=other)
 
     def __ror__(self: Self, other: ArrowExpr | bool | Any) -> Self:
-        return reuse_series_implementation(self, "__ror__", other=other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__or__(self)  # type: ignore[return-value]
 
     def __add__(self: Self, other: ArrowExpr | Any) -> Self:
         return reuse_series_implementation(self, "__add__", other)
 
     def __radd__(self: Self, other: ArrowExpr | Any) -> Self:
-        return reuse_series_implementation(self, "__radd__", other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__add__(self)  # type: ignore[return-value]
 
     def __sub__(self: Self, other: ArrowExpr | Any) -> Self:
         return reuse_series_implementation(self, "__sub__", other)
 
     def __rsub__(self: Self, other: ArrowExpr | Any) -> Self:
-        return reuse_series_implementation(self, "__rsub__", other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__sub__(self)  # type: ignore[return-value]
 
     def __mul__(self: Self, other: ArrowExpr | Any) -> Self:
         return reuse_series_implementation(self, "__mul__", other)
 
     def __rmul__(self: Self, other: ArrowExpr | Any) -> Self:
-        return reuse_series_implementation(self, "__rmul__", other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__mul__(self)  # type: ignore[return-value]
 
     def __pow__(self: Self, other: ArrowExpr | Any) -> Self:
         return reuse_series_implementation(self, "__pow__", other)
 
     def __rpow__(self: Self, other: ArrowExpr | Any) -> Self:
-        return reuse_series_implementation(self, "__rpow__", other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__pow__(self)  # type: ignore[return-value]
 
     def __floordiv__(self: Self, other: ArrowExpr | Any) -> Self:
         return reuse_series_implementation(self, "__floordiv__", other)
 
     def __rfloordiv__(self: Self, other: ArrowExpr | Any) -> Self:
-        return reuse_series_implementation(self, "__rfloordiv__", other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__floordiv__(self)  # type: ignore[return-value]
 
     def __truediv__(self: Self, other: ArrowExpr | Any) -> Self:
         return reuse_series_implementation(self, "__truediv__", other)
 
     def __rtruediv__(self: Self, other: ArrowExpr | Any) -> Self:
-        return reuse_series_implementation(self, "__rtruediv__", other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__truediv__(self)  # type: ignore[return-value]
 
     def __mod__(self: Self, other: ArrowExpr | Any) -> Self:
         return reuse_series_implementation(self, "__mod__", other)
 
     def __rmod__(self: Self, other: ArrowExpr | Any) -> Self:
-        return reuse_series_implementation(self, "__rmod__", other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__mod__(self)  # type: ignore[return-value]
 
     def __invert__(self: Self) -> Self:
         return reuse_series_implementation(self, "__invert__")
diff --git a/narwhals/_arrow/namespace.py b/narwhals/_arrow/namespace.py
index a20df3c41c..07fa7deb24 100644
--- a/narwhals/_arrow/namespace.py
+++ b/narwhals/_arrow/namespace.py
@@ -170,7 +170,7 @@ def _lit_arrow_series(_: ArrowDataFrame) -> ArrowSeries:
             depth=0,
             function_name="lit",
             root_names=None,
-            output_names=[_lit_arrow_series.__name__],
+            output_names=["literal"],
             backend_version=self._backend_version,
             dtypes=self._dtypes,
         )
diff --git a/narwhals/_arrow/series.py b/narwhals/_arrow/series.py
index a2caf77f41..ebfa5d6e58 100644
--- a/narwhals/_arrow/series.py
+++ b/narwhals/_arrow/series.py
@@ -96,78 +96,68 @@ def __len__(self: Self) -> int:
     def __eq__(self: Self, other: object) -> Self:  # type: ignore[override]
         import pyarrow.compute as pc
 
-        ser = self._native_series
-        other = validate_column_comparand(other)
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         return self._from_native_series(pc.equal(ser, other))
 
     def __ne__(self: Self, other: object) -> Self:  # type: ignore[override]
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        ser = self._native_series
-        other = validate_column_comparand(other)
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         return self._from_native_series(pc.not_equal(ser, other))
 
     def __ge__(self: Self, other: Any) -> Self:
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        ser = self._native_series
-        other = validate_column_comparand(other)
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         return self._from_native_series(pc.greater_equal(ser, other))
 
     def __gt__(self: Self, other: Any) -> Self:
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        ser = self._native_series
-        other = validate_column_comparand(other)
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         return self._from_native_series(pc.greater(ser, other))
 
     def __le__(self: Self, other: Any) -> Self:
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        ser = self._native_series
-        other = validate_column_comparand(other)
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         return self._from_native_series(pc.less_equal(ser, other))
 
     def __lt__(self: Self, other: Any) -> Self:
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        ser = self._native_series
-        other = validate_column_comparand(other)
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         return self._from_native_series(pc.less(ser, other))
 
     def __and__(self: Self, other: Any) -> Self:
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        ser = self._native_series
-        other = validate_column_comparand(other)
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         return self._from_native_series(pc.and_kleene(ser, other))
 
     def __rand__(self: Self, other: Any) -> Self:
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        ser = self._native_series
-        other = validate_column_comparand(other)
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         return self._from_native_series(pc.and_kleene(other, ser))
 
     def __or__(self: Self, other: Any) -> Self:
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        ser = self._native_series
-        other = validate_column_comparand(other)
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         return self._from_native_series(pc.or_kleene(ser, other))
 
     def __ror__(self: Self, other: Any) -> Self:
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        ser = self._native_series
-        other = validate_column_comparand(other)
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         return self._from_native_series(pc.or_kleene(other, ser))
 
     def __add__(self: Self, other: Any) -> Self:
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        other = validate_column_comparand(other)
-        return self._from_native_series(pc.add(self._native_series, other))
+        ser, other = validate_column_comparand(self, other, self._backend_version)
+        return self._from_native_series(pc.add(ser, other))
 
     def __radd__(self: Self, other: Any) -> Self:
         return self + other  # type: ignore[no-any-return]
@@ -175,8 +165,8 @@ def __radd__(self: Self, other: Any) -> Self:
     def __sub__(self: Self, other: Any) -> Self:
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        other = validate_column_comparand(other)
-        return self._from_native_series(pc.subtract(self._native_series, other))
+        ser, other = validate_column_comparand(self, other, self._backend_version)
+        return self._from_native_series(pc.subtract(ser, other))
 
     def __rsub__(self: Self, other: Any) -> Self:
         return (self - other) * (-1)  # type: ignore[no-any-return]
@@ -184,8 +174,8 @@ def __rsub__(self: Self, other: Any) -> Self:
     def __mul__(self: Self, other: Any) -> Self:
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        other = validate_column_comparand(other)
-        return self._from_native_series(pc.multiply(self._native_series, other))
+        ser, other = validate_column_comparand(self, other, self._backend_version)
+        return self._from_native_series(pc.multiply(ser, other))
 
     def __rmul__(self: Self, other: Any) -> Self:
         return self * other  # type: ignore[no-any-return]
@@ -193,33 +183,28 @@ def __rmul__(self: Self, other: Any) -> Self:
     def __pow__(self: Self, other: Any) -> Self:
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        ser = self._native_series
-        other = validate_column_comparand(other)
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         return self._from_native_series(pc.power(ser, other))
 
     def __rpow__(self: Self, other: Any) -> Self:
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        ser = self._native_series
-        other = validate_column_comparand(other)
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         return self._from_native_series(pc.power(other, ser))
 
     def __floordiv__(self: Self, other: Any) -> Self:
-        ser = self._native_series
-        other = validate_column_comparand(other)
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         return self._from_native_series(floordiv_compat(ser, other))
 
     def __rfloordiv__(self: Self, other: Any) -> Self:
-        ser = self._native_series
-        other = validate_column_comparand(other)
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         return self._from_native_series(floordiv_compat(other, ser))
 
     def __truediv__(self: Self, other: Any) -> Self:
         import pyarrow as pa  # ignore-banned-import()
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        ser = self._native_series
-        other = validate_column_comparand(other)
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         if not isinstance(other, (pa.Array, pa.ChunkedArray)):
             # scalar
             other = pa.scalar(other)
@@ -229,8 +214,7 @@ def __rtruediv__(self: Self, other: Any) -> Self:
         import pyarrow as pa  # ignore-banned-import()
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        ser = self._native_series
-        other = validate_column_comparand(other)
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         if not isinstance(other, (pa.Array, pa.ChunkedArray)):
             # scalar
             other = pa.scalar(other)
@@ -239,18 +223,16 @@ def __rtruediv__(self: Self, other: Any) -> Self:
     def __mod__(self: Self, other: Any) -> Self:
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        ser = self._native_series
-        other = validate_column_comparand(other)
         floor_div = (self // other)._native_series
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         res = pc.subtract(ser, pc.multiply(floor_div, other))
         return self._from_native_series(res)
 
     def __rmod__(self: Self, other: Any) -> Self:
         import pyarrow.compute as pc  # ignore-banned-import()
 
-        ser = self._native_series
-        other = validate_column_comparand(other)
         floor_div = (other // self)._native_series
+        ser, other = validate_column_comparand(self, other, self._backend_version)
         res = pc.subtract(other, pc.multiply(floor_div, ser))
         return self._from_native_series(res)
 
@@ -264,8 +246,10 @@ def len(self: Self) -> int:
 
     def filter(self: Self, other: Any) -> Self:
         if not (isinstance(other, list) and all(isinstance(x, bool) for x in other)):
-            other = validate_column_comparand(other)
-        return self._from_native_series(self._native_series.filter(other))
+            ser, other = validate_column_comparand(self, other, self._backend_version)
+        else:
+            ser = self._native_series
+        return self._from_native_series(ser.filter(other))
 
     def mean(self: Self) -> int:
         import pyarrow.compute as pc  # ignore-banned-import()
@@ -382,16 +366,17 @@ def scatter(self: Self, indices: int | Sequence[int], values: Any) -> Self:
         import pyarrow as pa  # ignore-banned-import
         import pyarrow.compute as pc  # ignore-banned-import
 
-        ca = self._native_series
-        mask = np.zeros(len(ca), dtype=bool)
+        mask = np.zeros(self.len(), dtype=bool)
         mask[indices] = True
         if isinstance(values, self.__class__):
-            values = validate_column_comparand(values)
+            ser, values = validate_column_comparand(self, values, self._backend_version)
+        else:
+            ser = self._native_series
         if isinstance(values, pa.ChunkedArray):
             values = values.combine_chunks()
         if not isinstance(values, pa.Array):
             values = pa.array(values)
-        result = pc.replace_with_mask(ca, mask, values.take(indices))
+        result = pc.replace_with_mask(ser, mask, values.take(indices))
         return self._from_native_series(result)
 
     def to_list(self: Self) -> list[Any]:
diff --git a/narwhals/_arrow/utils.py b/narwhals/_arrow/utils.py
index 4641bbb1f4..f8c25433c3 100644
--- a/narwhals/_arrow/utils.py
+++ b/narwhals/_arrow/utils.py
@@ -128,7 +128,9 @@ def narwhals_to_native_dtype(dtype: DType | type[DType], dtypes: DTypes) -> pa.D
     raise AssertionError(msg)
 
 
-def validate_column_comparand(other: Any) -> Any:
+def validate_column_comparand(
+    lhs: ArrowSeries, rhs: Any, backend_version: tuple[int, ...]
+) -> tuple[pa.ChunkedArray, Any]:
     """Validate RHS of binary operation.
 
     If the comparison isn't supported, return `NotImplemented` so that the
@@ -140,27 +142,47 @@ def validate_column_comparand(other: Any) -> Any:
     from narwhals._arrow.dataframe import ArrowDataFrame
     from narwhals._arrow.series import ArrowSeries
 
-    if isinstance(other, list):
-        if len(other) > 1:
-            if hasattr(other[0], "__narwhals_expr__") or hasattr(
-                other[0], "__narwhals_series__"
+    # If `rhs` is the output of an expression evaluation, then it is
+    # a list of Series. So, we verify that that list is of length-1,
+    # and take the first (and only) element.
+    if isinstance(rhs, list):
+        if len(rhs) > 1:
+            if hasattr(rhs[0], "__narwhals_expr__") or hasattr(
+                rhs[0], "__narwhals_series__"
             ):
                 # e.g. `plx.all() + plx.all()`
                 msg = "Multi-output expressions (e.g. `nw.all()` or `nw.col('a', 'b')`) are not supported in this context"
                 raise ValueError(msg)
-            msg = (
-                f"Expected scalar value, Series, or Expr, got list of : {type(other[0])}"
-            )
+            msg = f"Expected scalar value, Series, or Expr, got list of : {type(rhs[0])}"
             raise ValueError(msg)
-        other = other[0]
-    if isinstance(other, ArrowDataFrame):
+        rhs = rhs[0]
+
+    if isinstance(rhs, ArrowDataFrame):
         return NotImplemented
-    if isinstance(other, ArrowSeries):
-        if len(other) == 1:
+
+    if isinstance(rhs, ArrowSeries):
+        if len(rhs) == 1:
             # broadcast
-            return other[0]
-        return other._native_series
-    return other
+            return lhs._native_series, rhs[0]
+        if len(lhs) == 1:
+            # broadcast
+            import numpy as np  # ignore-banned-import
+            import pyarrow as pa  # ignore-banned-import
+
+            fill_value = lhs[0]
+            if backend_version < (13,) and hasattr(fill_value, "as_py"):
+                fill_value = fill_value.as_py()
+            left_result = pa.chunked_array(
+                [
+                    pa.array(
+                        np.full(shape=rhs.len(), fill_value=fill_value),
+                        type=lhs._native_series.type,
+                    )
+                ]
+            )
+            return left_result, rhs._native_series
+        return lhs._native_series, rhs._native_series
+    return lhs._native_series, rhs
 
 
 def validate_dataframe_comparand(
@@ -179,7 +201,7 @@ def validate_dataframe_comparand(
             import pyarrow as pa  # ignore-banned-import
 
             value = other._native_series[0]
-            if backend_version < (13,) and hasattr(value, "as_py"):  # pragma: no cover
+            if backend_version < (13,) and hasattr(value, "as_py"):
                 value = value.as_py()
             return pa.array(np.full(shape=length, fill_value=value))
         return other._native_series
@@ -321,7 +343,7 @@ def broadcast_series(series: list[ArrowSeries]) -> list[Any]:
         s_native = s._native_series
         if is_max_length_gt_1 and length == 1:
             value = s_native[0]
-            if s._backend_version < (13,) and hasattr(value, "as_py"):  # pragma: no cover
+            if s._backend_version < (13,) and hasattr(value, "as_py"):
                 value = value.as_py()
             reshaped.append(pa.array([value] * max_length, type=s_native.type))
         else:
diff --git a/narwhals/_dask/expr.py b/narwhals/_dask/expr.py
index 58e73792ac..d4e07c2c62 100644
--- a/narwhals/_dask/expr.py
+++ b/narwhals/_dask/expr.py
@@ -199,7 +199,7 @@ def __radd__(self, other: Any) -> Self:
             "__radd__",
             other,
             returns_scalar=False,
-        )
+        ).alias("literal")
 
     def __sub__(self, other: Any) -> Self:
         return self._from_call(
@@ -215,7 +215,7 @@ def __rsub__(self, other: Any) -> Self:
             "__rsub__",
             other,
             returns_scalar=False,
-        )
+        ).alias("literal")
 
     def __mul__(self, other: Any) -> Self:
         return self._from_call(
@@ -231,7 +231,7 @@ def __rmul__(self, other: Any) -> Self:
             "__rmul__",
             other,
             returns_scalar=False,
-        )
+        ).alias("literal")
 
     def __truediv__(self, other: Any) -> Self:
         return self._from_call(
@@ -247,7 +247,7 @@ def __rtruediv__(self, other: Any) -> Self:
             "__rtruediv__",
             other,
             returns_scalar=False,
-        )
+        ).alias("literal")
 
     def __floordiv__(self, other: Any) -> Self:
         return self._from_call(
@@ -263,7 +263,7 @@ def __rfloordiv__(self, other: Any) -> Self:
             "__rfloordiv__",
             other,
             returns_scalar=False,
-        )
+        ).alias("literal")
 
     def __pow__(self, other: Any) -> Self:
         return self._from_call(
@@ -279,7 +279,7 @@ def __rpow__(self, other: Any) -> Self:
             "__rpow__",
             other,
             returns_scalar=False,
-        )
+        ).alias("literal")
 
     def __mod__(self, other: Any) -> Self:
         return self._from_call(
@@ -295,7 +295,7 @@ def __rmod__(self, other: Any) -> Self:
             "__rmod__",
             other,
             returns_scalar=False,
-        )
+        ).alias("literal")
 
     def __eq__(self, other: DaskExpr) -> Self:  # type: ignore[override]
         return self._from_call(
@@ -353,13 +353,13 @@ def __and__(self, other: DaskExpr) -> Self:
             returns_scalar=False,
         )
 
-    def __rand__(self, other: DaskExpr) -> Self:  # pragma: no cover
+    def __rand__(self, other: DaskExpr) -> Self:
         return self._from_call(
             lambda _input, other: _input.__rand__(other),
             "__rand__",
             other,
             returns_scalar=False,
-        )
+        ).alias("literal")
 
     def __or__(self, other: DaskExpr) -> Self:
         return self._from_call(
@@ -369,13 +369,13 @@ def __or__(self, other: DaskExpr) -> Self:
             returns_scalar=False,
         )
 
-    def __ror__(self, other: DaskExpr) -> Self:  # pragma: no cover
+    def __ror__(self, other: DaskExpr) -> Self:
         return self._from_call(
             lambda _input, other: _input.__ror__(other),
             "__ror__",
             other,
             returns_scalar=False,
-        )
+        ).alias("literal")
 
     def __invert__(self: Self) -> Self:
         return self._from_call(
diff --git a/narwhals/_expression_parsing.py b/narwhals/_expression_parsing.py
index 0505637637..e8384165cf 100644
--- a/narwhals/_expression_parsing.py
+++ b/narwhals/_expression_parsing.py
@@ -235,7 +235,11 @@ def func(df: CompliantDataFrame) -> list[CompliantSeries]:
         if expr._output_names is not None and (
             [s.name for s in out] != expr._output_names
         ):  # pragma: no cover
-            msg = "Safety assertion failed, please report a bug to https://github.com/narwhals-dev/narwhals/issues"
+            msg = (
+                f"Safety assertion failed, please report a bug to https://github.com/narwhals-dev/narwhals/issues\n"
+                f"Expression output names: {expr._output_names}\n"
+                f"Series names: {[s.name for s in out]}"
+            )
             raise AssertionError(msg)
         return out
 
diff --git a/narwhals/_pandas_like/expr.py b/narwhals/_pandas_like/expr.py
index 182ea980fc..80648a90f8 100644
--- a/narwhals/_pandas_like/expr.py
+++ b/narwhals/_pandas_like/expr.py
@@ -159,55 +159,64 @@ def __and__(self, other: PandasLikeExpr | bool | Any) -> Self:
         return reuse_series_implementation(self, "__and__", other=other)
 
     def __rand__(self, other: Any) -> Self:
-        return reuse_series_implementation(self, "__rand__", other=other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__and__(self)  # type: ignore[no-any-return]
 
     def __or__(self, other: PandasLikeExpr | bool | Any) -> Self:
         return reuse_series_implementation(self, "__or__", other=other)
 
     def __ror__(self, other: Any) -> Self:
-        return reuse_series_implementation(self, "__ror__", other=other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__or__(self)  # type: ignore[no-any-return]
 
     def __add__(self, other: PandasLikeExpr | Any) -> Self:
         return reuse_series_implementation(self, "__add__", other=other)
 
     def __radd__(self, other: Any) -> Self:
-        return reuse_series_implementation(self, "__radd__", other=other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__add__(self)  # type: ignore[no-any-return]
 
     def __sub__(self, other: PandasLikeExpr | Any) -> Self:
         return reuse_series_implementation(self, "__sub__", other=other)
 
     def __rsub__(self, other: Any) -> Self:
-        return reuse_series_implementation(self, "__rsub__", other=other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__sub__(self)  # type: ignore[no-any-return]
 
     def __mul__(self, other: PandasLikeExpr | Any) -> Self:
         return reuse_series_implementation(self, "__mul__", other=other)
 
     def __rmul__(self, other: Any) -> Self:
-        return reuse_series_implementation(self, "__rmul__", other=other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__mul__(self)  # type: ignore[no-any-return]
 
     def __truediv__(self, other: PandasLikeExpr | Any) -> Self:
         return reuse_series_implementation(self, "__truediv__", other=other)
 
     def __rtruediv__(self, other: Any) -> Self:
-        return reuse_series_implementation(self, "__rtruediv__", other=other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__truediv__(self)  # type: ignore[no-any-return]
 
     def __floordiv__(self, other: PandasLikeExpr | Any) -> Self:
         return reuse_series_implementation(self, "__floordiv__", other=other)
 
     def __rfloordiv__(self, other: Any) -> Self:
-        return reuse_series_implementation(self, "__rfloordiv__", other=other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__floordiv__(self)  # type: ignore[no-any-return]
 
     def __pow__(self, other: PandasLikeExpr | Any) -> Self:
         return reuse_series_implementation(self, "__pow__", other=other)
 
     def __rpow__(self, other: Any) -> Self:
-        return reuse_series_implementation(self, "__rpow__", other=other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__pow__(self)  # type: ignore[no-any-return]
 
     def __mod__(self, other: PandasLikeExpr | Any) -> Self:
         return reuse_series_implementation(self, "__mod__", other=other)
 
     def __rmod__(self, other: Any) -> Self:
-        return reuse_series_implementation(self, "__rmod__", other=other)
+        other = self.__narwhals_namespace__().lit(other, dtype=None)
+        return other.__mod__(self)  # type: ignore[no-any-return]
 
     # Unary
 
diff --git a/narwhals/_pandas_like/namespace.py b/narwhals/_pandas_like/namespace.py
index b001f19db3..60f5fa24f4 100644
--- a/narwhals/_pandas_like/namespace.py
+++ b/narwhals/_pandas_like/namespace.py
@@ -155,7 +155,7 @@ def _lit_pandas_series(df: PandasLikeDataFrame) -> PandasLikeSeries:
             depth=0,
             function_name="lit",
             root_names=None,
-            output_names=[_lit_pandas_series.__name__],
+            output_names=["literal"],
             implementation=self._implementation,
             backend_version=self._backend_version,
             dtypes=self._dtypes,
@@ -501,8 +501,9 @@ def __call__(self, df: PandasLikeDataFrame) -> list[PandasLikeSeries]:
             )
         value_series = cast(PandasLikeSeries, value_series)
 
-        value_series_native = value_series._native_series
-        condition_native = validate_column_comparand(value_series_native.index, condition)
+        value_series_native, condition_native = validate_column_comparand(
+            value_series, condition
+        )
 
         if self._otherwise_value is None:
             return [
diff --git a/narwhals/_pandas_like/series.py b/narwhals/_pandas_like/series.py
index 426e828b11..ef8e784cff 100644
--- a/narwhals/_pandas_like/series.py
+++ b/narwhals/_pandas_like/series.py
@@ -218,9 +218,9 @@ def scatter(self, indices: int | Sequence[int], values: Any) -> Self:
         if isinstance(values, self.__class__):
             # .copy() is necessary in some pre-2.2 versions of pandas to avoid
             # `values` also getting modified (!)
-            values = validate_column_comparand(self._native_series.index, values).copy()
+            _, values = validate_column_comparand(self, values)
             values = set_axis(
-                values,
+                values.copy(),
                 self._native_series.index[indices],
                 implementation=self._implementation,
                 backend_version=self._backend_version,
@@ -298,135 +298,135 @@ def arg_true(self) -> PandasLikeSeries:
     def filter(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
         if not (isinstance(other, list) and all(isinstance(x, bool) for x in other)):
-            other = validate_column_comparand(self._native_series.index, other)
+            ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.loc[other].rename(ser.name, copy=False))
 
     def __eq__(self, other: object) -> PandasLikeSeries:  # type: ignore[override]
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__eq__(other).rename(ser.name, copy=False))
 
     def __ne__(self, other: object) -> PandasLikeSeries:  # type: ignore[override]
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__ne__(other).rename(ser.name, copy=False))
 
     def __ge__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__ge__(other).rename(ser.name, copy=False))
 
     def __gt__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__gt__(other).rename(ser.name, copy=False))
 
     def __le__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__le__(other).rename(ser.name, copy=False))
 
     def __lt__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__lt__(other).rename(ser.name, copy=False))
 
     def __and__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__and__(other).rename(ser.name, copy=False))
 
     def __rand__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
-        return self._from_native_series(ser.__rand__(other).rename(ser.name, copy=False))
+        ser, other = validate_column_comparand(self, other)
+        return self._from_native_series(ser.__and__(other).rename(ser.name, copy=False))
 
     def __or__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__or__(other).rename(ser.name, copy=False))
 
     def __ror__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
-        return self._from_native_series(ser.__ror__(other).rename(ser.name, copy=False))
+        ser, other = validate_column_comparand(self, other)
+        return self._from_native_series(ser.__or__(other).rename(ser.name, copy=False))
 
     def __add__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__add__(other).rename(ser.name, copy=False))
 
     def __radd__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__radd__(other).rename(ser.name, copy=False))
 
     def __sub__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__sub__(other).rename(ser.name, copy=False))
 
     def __rsub__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__rsub__(other).rename(ser.name, copy=False))
 
     def __mul__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__mul__(other).rename(ser.name, copy=False))
 
     def __rmul__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__rmul__(other).rename(ser.name, copy=False))
 
     def __truediv__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(
             ser.__truediv__(other).rename(ser.name, copy=False)
         )
 
     def __rtruediv__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(
             ser.__rtruediv__(other).rename(ser.name, copy=False)
         )
 
     def __floordiv__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(
             ser.__floordiv__(other).rename(ser.name, copy=False)
         )
 
     def __rfloordiv__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(
             ser.__rfloordiv__(other).rename(ser.name, copy=False)
         )
 
     def __pow__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__pow__(other).rename(ser.name, copy=False))
 
     def __rpow__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__rpow__(other).rename(ser.name, copy=False))
 
     def __mod__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__mod__(other).rename(ser.name, copy=False))
 
     def __rmod__(self, other: Any) -> PandasLikeSeries:
         ser = self._native_series
-        other = validate_column_comparand(self._native_series.index, other)
+        ser, other = validate_column_comparand(self, other)
         return self._from_native_series(ser.__rmod__(other).rename(ser.name, copy=False))
 
     # Unary
@@ -738,9 +738,8 @@ def quantile(
         return self._native_series.quantile(q=quantile, interpolation=interpolation)
 
     def zip_with(self: Self, mask: Any, other: Any) -> PandasLikeSeries:
-        ser = self._native_series
-        mask = validate_column_comparand(ser.index, mask)
-        other = validate_column_comparand(ser.index, other)
+        ser, mask = validate_column_comparand(self, mask)
+        _, other = validate_column_comparand(self, other)
         res = ser.where(mask, other)
         return self._from_native_series(res)
 
diff --git a/narwhals/_pandas_like/utils.py b/narwhals/_pandas_like/utils.py
index 44bfc34b7a..79be11aaa4 100644
--- a/narwhals/_pandas_like/utils.py
+++ b/narwhals/_pandas_like/utils.py
@@ -79,7 +79,7 @@
 PATTERN_PA_DURATION = re.compile(PA_DURATION_RGX, re.VERBOSE)
 
 
-def validate_column_comparand(index: Any, other: Any) -> Any:
+def validate_column_comparand(lhs: PandasLikeSeries, rhs: Any) -> tuple[pd.Series, Any]:
     """Validate RHS of binary operation.
 
     If the comparison isn't supported, return `NotImplemented` so that the
@@ -91,35 +91,56 @@ def validate_column_comparand(index: Any, other: Any) -> Any:
     from narwhals._pandas_like.dataframe import PandasLikeDataFrame
     from narwhals._pandas_like.series import PandasLikeSeries
 
-    if isinstance(other, list):
-        if len(other) > 1:
-            if hasattr(other[0], "__narwhals_expr__") or hasattr(
-                other[0], "__narwhals_series__"
+    # If `rhs` is the output of an expression evaluation, then it is
+    # a list of Series. So, we verify that that list is of length-1,
+    # and take the first (and only) element.
+    if isinstance(rhs, list):
+        if len(rhs) > 1:
+            if hasattr(rhs[0], "__narwhals_expr__") or hasattr(
+                rhs[0], "__narwhals_series__"
             ):
                 # e.g. `plx.all() + plx.all()`
                 msg = "Multi-output expressions (e.g. `nw.all()` or `nw.col('a', 'b')`) are not supported in this context"
                 raise ValueError(msg)
-            msg = (
-                f"Expected scalar value, Series, or Expr, got list of : {type(other[0])}"
-            )
+            msg = f"Expected scalar value, Series, or Expr, got list of : {type(rhs[0])}"
             raise ValueError(msg)
-        other = other[0]
-    if isinstance(other, PandasLikeDataFrame):
+        rhs = rhs[0]
+
+    lhs_index = lhs._native_series.index
+
+    if isinstance(rhs, PandasLikeDataFrame):
         return NotImplemented
-    if isinstance(other, PandasLikeSeries):
-        if other.len() == 1:
+
+    if isinstance(rhs, PandasLikeSeries):
+        rhs_index = rhs._native_series.index
+        if rhs.len() == 1:
             # broadcast
-            s = other._native_series
-            return s.__class__(s.iloc[0], index=index, dtype=s.dtype)
-        if other._native_series.index is not index:
-            return set_axis(
-                other._native_series,
-                index,
-                implementation=other._implementation,
-                backend_version=other._backend_version,
+            s = rhs._native_series
+            return (
+                lhs._native_series,
+                s.__class__(s.iloc[0], index=lhs_index, dtype=s.dtype),
             )
-        return other._native_series
-    return other
+        if lhs.len() == 1:
+            # broadcast
+            s = lhs._native_series
+            return (
+                s.__class__(s.iloc[0], index=rhs_index, dtype=s.dtype, name=s.name),
+                rhs._native_series,
+            )
+        if rhs._native_series.index is not lhs_index:
+            return (
+                lhs._native_series,
+                set_axis(
+                    rhs._native_series,
+                    lhs_index,
+                    implementation=rhs._implementation,
+                    backend_version=rhs._backend_version,
+                ),
+            )
+        return (lhs._native_series, rhs._native_series)
+
+    # `rhs` must be scalar, so just leave it as-is
+    return lhs._native_series, rhs
 
 
 def validate_dataframe_comparand(index: Any, other: Any) -> Any:
diff --git a/narwhals/_polars/series.py b/narwhals/_polars/series.py
index a0df340d2f..492913227e 100644
--- a/narwhals/_polars/series.py
+++ b/narwhals/_polars/series.py
@@ -192,9 +192,11 @@ def __pow__(self, other: PolarsSeries | Any) -> Self:
         )
 
     def __rpow__(self, other: PolarsSeries | Any) -> Self:
-        return self._from_native_series(
-            self._native_series.__rpow__(extract_native(other))
-        )
+        result = self._native_series.__rpow__(extract_native(other))
+        if self._backend_version < (16, 1):
+            # Explicitly set alias to work around https://github.com/pola-rs/polars/issues/20071
+            result = result.alias(self.name)
+        return self._from_native_series(result)
 
     def __invert__(self) -> Self:
         return self._from_native_series(self._native_series.__invert__())
diff --git a/narwhals/series.py b/narwhals/series.py
index 6d4c5e17ca..6c011610ed 100644
--- a/narwhals/series.py
+++ b/narwhals/series.py
@@ -2037,11 +2037,21 @@ def __and__(self, other: Any) -> Self:
             self._compliant_series.__and__(self._extract_native(other))
         )
 
+    def __rand__(self, other: Any) -> Self:
+        return self._from_compliant_series(
+            self._compliant_series.__rand__(self._extract_native(other))
+        )
+
     def __or__(self, other: Any) -> Self:
         return self._from_compliant_series(
             self._compliant_series.__or__(self._extract_native(other))
         )
 
+    def __ror__(self, other: Any) -> Self:
+        return self._from_compliant_series(
+            self._compliant_series.__ror__(self._extract_native(other))
+        )
+
     # unary
     def __invert__(self) -> Self:
         return self._from_compliant_series(self._compliant_series.__invert__())
diff --git a/pyproject.toml b/pyproject.toml
index 3e43940c19..79ae858d3f 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -148,8 +148,9 @@ exclude_also = [
   "if (:?self._)?implementation is Implementation.MODIN",
   "if (:?self._)?implementation is Implementation.CUDF",
   'request.applymarker\(pytest.mark.xfail\)',
-  'if self._backend_version < ',
-  'if "cudf" in str\(constructor',
+  'if \w+._backend_version < ',
+  'if backend_version <',
+  'if "cudf" in str\(constructor'
 ]
 
 [tool.mypy]
diff --git a/tests/expr_and_series/arithmetic_test.py b/tests/expr_and_series/arithmetic_test.py
index 95172bd2cb..12f931baa6 100644
--- a/tests/expr_and_series/arithmetic_test.py
+++ b/tests/expr_and_series/arithmetic_test.py
@@ -74,8 +74,8 @@ def test_right_arithmetic_expr(
 
     data = {"a": [1, 2, 3]}
     df = nw.from_native(constructor(data))
-    result = df.select(a=getattr(nw.col("a"), attr)(rhs))
-    assert_equal_data(result, {"a": expected})
+    result = df.select(getattr(nw.col("a"), attr)(rhs))
+    assert_equal_data(result, {"literal": expected})
 
 
 @pytest.mark.parametrize(
@@ -135,8 +135,9 @@ def test_right_arithmetic_series(
 
     data = {"a": [1, 2, 3]}
     df = nw.from_native(constructor_eager(data), eager_only=True)
-    result = df.select(a=getattr(df["a"], attr)(rhs))
-    assert_equal_data(result, {"a": expected})
+    result_series = getattr(df["a"], attr)(rhs)
+    assert result_series.name == "a"
+    assert_equal_data({"a": result_series}, {"a": expected})
 
 
 def test_truediv_same_dims(
@@ -218,3 +219,65 @@ def test_mod(left: int, right: int) -> None:
         nw.col("a") % right
     )
     assert_equal_data(result, expected)
+
+
+@pytest.mark.parametrize(
+    ("attr", "lhs", "expected"),
+    [
+        ("__add__", nw.lit(1), [2, 3, 5]),
+        ("__sub__", nw.lit(1), [0, -1, -3]),
+        ("__mul__", nw.lit(2), [2, 4, 8]),
+        ("__truediv__", nw.lit(2.0), [2, 1, 0.5]),
+        ("__truediv__", nw.lit(1), [1, 0.5, 0.25]),
+        ("__floordiv__", nw.lit(2), [2, 1, 0]),
+        ("__mod__", nw.lit(3), [0, 1, 3]),
+        ("__pow__", nw.lit(2), [2, 4, 16]),
+    ],
+)
+def test_arithmetic_expr_left_literal(
+    attr: str,
+    lhs: Any,
+    expected: list[Any],
+    constructor: Constructor,
+    request: pytest.FixtureRequest,
+) -> None:
+    if attr == "__mod__" and any(
+        x in str(constructor) for x in ["pandas_pyarrow", "modin"]
+    ):
+        request.applymarker(pytest.mark.xfail)
+
+    data = {"a": [1.0, 2, 4]}
+    df = nw.from_native(constructor(data))
+    result = df.select(getattr(lhs, attr)(nw.col("a")))
+    assert_equal_data(result, {"literal": expected})
+
+
+@pytest.mark.parametrize(
+    ("attr", "lhs", "expected"),
+    [
+        ("__add__", nw.lit(1), [2, 3, 5]),
+        ("__sub__", nw.lit(1), [0, -1, -3]),
+        ("__mul__", nw.lit(2), [2, 4, 8]),
+        ("__truediv__", nw.lit(2.0), [2, 1, 0.5]),
+        ("__truediv__", nw.lit(1), [1, 0.5, 0.25]),
+        ("__floordiv__", nw.lit(2), [2, 1, 0]),
+        ("__mod__", nw.lit(3), [0, 1, 3]),
+        ("__pow__", nw.lit(2), [2, 4, 16]),
+    ],
+)
+def test_arithmetic_series_left_literal(
+    attr: str,
+    lhs: Any,
+    expected: list[Any],
+    constructor_eager: ConstructorEager,
+    request: pytest.FixtureRequest,
+) -> None:
+    if attr == "__mod__" and any(
+        x in str(constructor_eager) for x in ["pandas_pyarrow", "modin"]
+    ):
+        request.applymarker(pytest.mark.xfail)
+
+    data = {"a": [1.0, 2, 4]}
+    df = nw.from_native(constructor_eager(data))
+    result = df.select(getattr(lhs, attr)(nw.col("a")))
+    assert_equal_data(result, {"literal": expected})
diff --git a/tests/expr_and_series/operators_test.py b/tests/expr_and_series/operators_test.py
index 5506e6a8d7..ff01747a60 100644
--- a/tests/expr_and_series/operators_test.py
+++ b/tests/expr_and_series/operators_test.py
@@ -65,6 +65,25 @@ def test_logic_operators_expr(
     assert_equal_data(result, {"a": expected})
 
 
+@pytest.mark.parametrize(
+    ("operator", "expected"),
+    [
+        ("__and__", [False, False, False, False]),
+        ("__rand__", [False, False, False, False]),
+        ("__or__", [True, True, False, False]),
+        ("__ror__", [True, True, False, False]),
+    ],
+)
+def test_logic_operators_expr_scalar(
+    constructor: Constructor, operator: str, expected: list[bool]
+) -> None:
+    data = {"a": [True, True, False, False]}
+    df = nw.from_native(constructor(data))
+
+    result = df.select(a=getattr(nw.col("a"), operator)(False))  # noqa: FBT003
+    assert_equal_data(result, {"a": expected})
+
+
 @pytest.mark.parametrize(
     ("operator", "expected"),
     [
@@ -110,7 +129,9 @@ def test_comparand_operators_series(
     ("operator", "expected"),
     [
         ("__and__", [True, False, False, False]),
+        ("__rand__", [True, False, False, False]),
         ("__or__", [True, True, True, False]),
+        ("__ror__", [True, True, True, False]),
     ],
 )
 def test_logic_operators_series(
diff --git a/tests/frame/lit_test.py b/tests/frame/lit_test.py
index 2b0332a5e5..f51bd5c76a 100644
--- a/tests/frame/lit_test.py
+++ b/tests/frame/lit_test.py
@@ -62,3 +62,33 @@ def test_lit_out_name(constructor: Constructor) -> None:
         "literal": [2, 2, 2],
     }
     assert_equal_data(result, expected)
+
+
+@pytest.mark.parametrize(
+    ("col_name", "expr", "expected_result"),
+    [
+        ("left_lit", nw.lit(1) + nw.col("a"), [2, 4, 3]),
+        ("right_lit", nw.col("a") + nw.lit(1), [2, 4, 3]),
+        ("left_lit_with_agg", nw.lit(1) + nw.col("a").mean(), [3]),
+        ("right_lit_with_agg", nw.col("a").mean() - nw.lit(1), [1]),
+        ("left_scalar", 1 + nw.col("a"), [2, 4, 3]),
+        ("right_scalar", nw.col("a") + 1, [2, 4, 3]),
+        ("left_scalar_with_agg", 1 + nw.col("a").mean(), [3]),
+        ("right_scalar_with_agg", nw.col("a").mean() - 1, [1]),
+    ],
+)
+def test_lit_operation(
+    constructor: Constructor,
+    col_name: str,
+    expr: nw.Expr,
+    expected_result: list[int],
+    request: pytest.FixtureRequest,
+) -> None:
+    if "dask_lazy_p2" in str(constructor) and "lit_with_agg" in col_name:
+        request.applymarker(pytest.mark.xfail)
+    data = {"a": [1, 3, 2]}
+    df_raw = constructor(data)
+    df = nw.from_native(df_raw).lazy()
+    result = df.select(expr.alias(col_name))
+    expected = {col_name: expected_result}
+    assert_equal_data(result, expected)
diff --git a/tests/utils.py b/tests/utils.py
index 90143959dc..f9b493add2 100644
--- a/tests/utils.py
+++ b/tests/utils.py
@@ -62,7 +62,7 @@ def assert_equal_data(result: Any, expected: dict[str, Any]) -> None:
         result = result.collect()
     if hasattr(result, "columns"):
         for key in result.columns:
-            assert key in expected
+            assert key in expected, (key, expected)
     result = {key: _to_comparable_list(result[key]) for key in expected}
     for key in expected:
         result_key = result[key]