In general terms, a motorcycle's physical size is smaller than 4 wheel vehicles.
However, motorcycles require just as much of the road to be operated safely. To stop or avoid a hazard, lane positioning etc. As an example.
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Motorcycles will in fact take up less space than a single occupant vehicle in every conceivable scenario.
However, this analysis isn't a good argument in favour of allowing MCs on HOVs for a few reasons;
1- The method the gov't chose to increase throughput is by increasing the number of occupants per vehicle, not reducing the road space each occupant requires as in my math (but that's daft, because nobody ever sat in traffic complaining that there aren't enough people in the cars around them!)
2- The decision on which vehicles are excluded from the HOV isn't based on a formula like my graph because that would make it impossible to enforce. Instead it's based on gross generalizations according to vehicle type and number of occupants, which enforcement officers can easily distinguish.
3- There are already exception for other single occupant vehicles, such as buses (which makes sense since they end up saving space overall when the round trip empty/full of passengers is considered), and 'green' cars (which makes sense because politicians love to coat themselves in green policy for when election time rolls around).
Having said all that, it still leaves plenty of scope for allowing motorcycles to use HOV lanes.
Single occupant bikes use less road space than single occupant cars. They gov't doesn't want to hear that argument but they're wrong as the benefit is real. The other point is that motorcycles are pretty uncommon on the road so allowing them on HOVs wouldn't compromise the element of exclusivity that is essential to allowing them to flow faster than regular traffic. And finally, since exceptions can be made to the single occupant rule, an exception for motorcycles is justified on the basis of improving safety for riders. Of course, motorcycles are easily distinguishable from all other forms of traffic so enforcement of HOV restrictions wouldn't be compromised by allowing MCs.
It's not like we'd be inventing anything that isn't done in dozens of other jurisdictions around the world, BTW.