JR pricing question

I'm wondering why a JR ticket from Iidabashi (in Tokyo) to Yokohama costs \540, while a a ticket from Iidabashi to Shinagawa costs \190 and a ticket further on to Yokohama from there costs \280, i.e. \470 in total. Any reason for that strange pricing?

That is because some exceptional fares are defined for some popular sections in Japan, especially in large urban areas. Often it has to do with keeping the fares competitive with the fares of other railway operators.

In this specific case, the Shinagawa-Yokohama section is made cheaper to compete with the fares of Keikyu Railways that runs parallel to the JR line.

{JR base fares}

0. Specified fares set lower or higher for certain sections
: e.g. 280 yen for Shinagawa -- Yokohama (of JR-East), set lower than normal 380 yen
: e.g. Additional 210 yen for a section including Hineno -- Kansai-airport (of JR-West)

1. Fares set for sections inside the loop of Yamanote Line (of JR-East) / of Osaka Loop Line (of JR-West)
: The rate is lowest among those of Categories 1 to 4.
: e.g. 190 yen for Iidabashi -- Shinagawa (of JR-East)

2. Fares set for sections within the designated area around Tokyo (of JR-East) / around Osaka (of JR-West)
: The rate is second lowest, and is applied to sections except those of Category 1.
: e.g. 540 yen for Iidabashi -- Yokohama (of JR-East)

3. Fares set for sections of arterial lines
: The rate is applied to sections except those of Categories 1 and 2.
: e.g. 1,450 yen for Iidabashi -- Odawara (of JR-East)

4. Fares set for sections of rural lines
: The rate is highest among those of Categories 1 to 4.

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Basis of the system of JR base fares was made in the age of JNR [Kokutetsu], before it was privatized in 1987 into JR companies including 6 regional passenger rail companies.
I suppose some historical facts are on the background of this complicated system.
JNR was a state-held company, whose costs were NOT covered with taxes. It was not a rail constructor but only a rail operator. While it faced stiff competitions in urban areas, it had to manage non-cost-efficient rural lines.