If the pedometer is reset and already on before Shabbat starts, am I allowed to attach it to my person and walk with it on Shabbat, within an eruv? It is electric, and it appears to count steps with a small shaker, although I cannot tell if this shaker completes a circuit to count.
This sounds like a classic example of a p'sik reisha, something that will happen inevitably, although it is the indirect result of your actions.
Most pedometers have a digital display that shows the steps taken. If that is the case, the changing display would be a Shabbos violation, of either Rabbinic or Biblical magnitude depending on differing opinions (the Chazon Ish holds completing a circuit is a Biblical prohibition, others disagreed).
Even in a Rabbinical prohibition, the Magen Avraham (O.C. 314:5) writes that it is prohibited.
If the display is not active without pushing a button, the following case may be relevant: The water meters in Baltimore have an active meter which digitally records the water usage to a display. However, (with the intervention of R' Moshe Heinemann) the digital display is not active until the cover of the display is opened. R' Heinemann ruled that even though the digital system is recording the information, since there is no output, it is not a problem to flush your toilet on Shabbos in Baltimore (phew!). (Source: I was in the room when R' Heinemann discussed this in a halacha shiur.) This would seem to be similar.
As always, CYLOR.
According to most opinions turning on a digital screen on shabbos might be a problem of Nolad. So it's already a safek d'rabonon, secondly if the screen is already on before shabbos then it's no problem at all becaus even if you say TURNING ON the screen is Nolad, there is no issur in adding to Nolad. The Gemara (I forgot exactly where) states an example of spraying a garment with incense on shabbos and that it is forbidden. However if the garment currently had incense on it already then there is no issur of adding more to it because there's no issur of adding to the act of Nolad.