  A weak measurement performed on a pre- and post-selected quantum system can
result in an average value that lies outside of the observable's spectrum. This
effect, usually referred to as an "anomalous weak value", is generally believed
to be possible only when a non-trivial post-selection is performed, i.e., when
only a particular subset of the data is considered. Here we show, however, that
this is not the case in general: in scenarios in which several weak
measurements are sequentially performed, an anomalous weak value can be
obtained without post-selection, i.e., without discarding any data. We discuss
several questions that this raises about the subtle relation between weak
values and pointer positions for sequential weak measurements. Finally, we
consider some implications of our results for the problem of distinguishing
different causal structures.
