I don't really mean to ask the question as it is typed, as I know for a fact that it can, however, Ameren Illinois recently installed (3) GE M400R3 with the White/Red 40 NEMA Label, which is the Label for PSMH, but they put 400W HPS Lamps in the fixtures instead of 400W PSMH Lamps.  These are brand new luminaires, probably no more than 4 months old, and all 3 are pretty dim.  I'd say, if I had to guesstimate, that the light output from each one is between 200-250W of light.  Now, there is also a single GE PF-400 with the White/Red PSMH NEMA Label (40) and there is a 400W HPS lamp in that fixture as well, and it warms up to the full intensity.  So I guess my REAL question is, Will it cause damage to the Ballast/Capacitor/Ignitor  to run a 400W HPS Lamp in a 400W PSMH Luminaire?  Because, as I said, it works fine in the PF-400, but the M400R3s, ALL 3 of them, do NOT warm up to their full intensity.  If it were only one of them that were like that, I would assume it is a fixture issue, but all 3 were installed on the same day, and all 3 are rather dim considering they are supposed to be 400 Watts.  I know full well that it is not putting out 400 Watts worth of Light.  The picture I attached is the label on all of the luminaires I have mentioned, except they read 40 instead of 25.

I have heard of metal halides lamps for use on HPS ballasts, but not the other way around.

I have heard of metal halides lamps for use on HPS ballasts, but not the other way around.

Yep, I have looked at these 3 (4 actually including the PF-400) several times during the day, and several times at night, and the only one that seems to be fully accepting the 400W HPS is the PF-400.  The 3 M400R3s aren't putting out 400 Watts worth of HPS light.  Which leads me to ask, Why would the Lineman install a PSMH Luminaire, and not put in a PSMH Lamp?  Why not just install 3 M400R3s that were built for 400W HPS if that was his intent?

I have tried running a 400W HPS bulb from a 400W PS MH ballast-indeed-the HPS bulb doesn't go to full brightness.Just an experiment.Use the 400W Venture PSMH bulb instead-MUCH better!Maybe the linemen that put in those HPS bulbs thought they would give longer life then the 400W PSMH?

I have tried running a 400W HPS bulb from a 400W PS MH ballast-indeed-the HPS bulb doesn't go to full brightness.Just an experiment.Use the 400W Venture PSMH bulb instead-MUCH better!Maybe the linemen that put in those HPS bulbs thought they would give longer life then the 400W PSMH?

I would think the exact opposite in that it would shorten the life/damage the bulb.  Also, why does the PF-400 light up to full intensitu though?  It just seems to be the 3 M400R3s that have a problem warming up to the full intensity.  As a matter of fact, they are so dim, they probably would have had better results using an HPS rated M250R2 (250 Watt HPS) or even a 100 Watt 201SA Bucket Light.  Before they put the M400R3s up, there were 175W Merc Buckets.  This particular lineman, about a year ago, and a half, replaced a 175w GE Merc 201SA with a 250W Sodium M250R2, and it is BRIGHT!!!  He even took it one step further, and replaced the 250W Merc Bucket right down the street with a 250W Sodium M250R2, and again.  BRIGHT!!!!  So why he did this M400R3 job with Sodium lamps in a PSMH Luminaire is beyond me.  

@tolivac: Yeah, the lower power to the lamp will cause it to sputter more and degrade the electrodes quicker.
@M250R201SA: 250w buckets lights seem to be a common occurrence in your area, hopefully you can get the two you've been looking after.
Ameren Illinois here in Springfield don't seem to be that dumb, however, I have seen instances where there are oddly placed NEMA buckets. An example of this is one of a long truss arm hanging over a busy intersection, versus a normal cobrahead, which would direct more light down and less would be wasted. I also saw a lone bucket sharing a pole with a Cree LED light on state fairgrounds, but thankfully lived on!
On another note, there may be a special magnetic ballast designed for the lamps as well as the , or the ballast could very likely be electronic flavored.

Not special, just a ballast for the European lamps. Over here HPS and Pulse MH use the same gear by design

I believe the only workable substitute in North America is running a 150 w HPS on a 150 w PSMH ballast (not the other way around). Otherwise, there is no combination that will not drastically shorten the life of the lamp (and ballast and ignitor too).

150 S55 or S56 ?

I have a 420 Watt PSMH bulb from Venture Lighting.  I just need to find a fixture for it. 

Any HPS lamp on a PSMH ballast will be underdriven considerably, HPS prefer low voltage high current, whereas MH are the opposite. The 150w PSMH ballast will not operate a 150w HPS lamp at full intensity, ive tried it.

Any HPS lamp on a PSMH ballast will be underdriven considerably, HPS prefer low voltage high current, whereas MH are the opposite. The 150w PSMH ballast will not operate a 150w HPS lamp at full intensity, ive tried it.

The pulse MH are all designed with the arc voltages of 70..90V (depend on wattage, higher wattage means higher arc voltage).

For wattages 100W and below and S55 the HPS are designed for just a series reactor, so the lamp arc voltage is limited to about 55V, hence the higher current.
The S56 is the same as poulse MH 150W (77V, 1.8A arc). The 150W is a bit mess, as it is offered in two forms, completely not compatible with each other (the S55 vs S56).
With higher wattages the HPS arc voltage become higher (but not sure, if the 250W isn't still the same 77V).

So higher wattages than 250W means the HPS operated on an MH ballast would be overdriven and maybe unstable arc (too high current, too low OCV)

The 400W HPS on an MH ballast may start, warm up way faster (as it would be overloaded in that stage), but then most likely cycle (insufficient OCV of the ballast to hold the arc in a stable manner)

The S56 150W HPS lamps and over, have higher lamp voltage. pulse-start MH lamps, that aren't designed for HPS ballasts, will be underdriven because of lower current and not because of lower voltage.

Oh yes,forgot about the running of discharge bulbs below their rating.This happens with xenon lamps in cinema projectors that have a variable ballast on the bulb.Some projectionists are told to run the bulb lower with thoughts of longer life-but not desirable.Also the xenon projection bulbs get unstable arcs when run at too low amperage.The arc magnet in the lamphouse can't stabliize the arc-appears as a fluctuating ,flickering picture to the audience.The xenon bulb electrodes-esp the cathode since those are DC lamps will get damaged.There is a min and max operating range for those bulbs-could apply to gen lighting discharge bulbs,too.I did not continue to run the HPS bulb on the PSMH ballast-the light output is too low and yellow to be useable.So the lineman in the above examples could end up replacing the HPS bulbs sooner then he realizes-better to use the PSMH bulb as the fixture and ballast call for.

The Lamp(s) and Luminaire(s) in question are

3- 400 Watt  Lamps
   installed in
3- 400 Watt  General Electric M400R3 Luminaires

Would it make any difference if I were to call the utility and report this, or would it be futile.
I will try and get photos of one of the GE M400R3s rated for 400 Watt    operating this evening with their  , and of a GE M400R3 rated for 400 Watt  with a  lamp installed and upload them.