What are the different measures of inflation, and are we being conned?

The UK uses three measures and each has its fans, but it does seem unnecessarily complicated

MPs press Treasury to abandon 'absurd' inflation measure

Is inflation really that difficult to calculate?
It seems so. There are three main estimates produced by the ONS: the consumer prices index (CPI); consumer prices index including owner-occupiers' housing costs (CPIH): and the retail prices index (RPI). The rates for December 2018 - January's figures are out tomorrow - show CPI is 2.1%, CPIH is 2.0%, and RPI is 2.7%. The "headline" rate that tends to be used by the government and media is the CPI. Statisticians appear to prefer CPIH, while RPI is either hated or loved depending on whether it makes you a winner or a loser.

Are we being conned on the real rate?
That's a constant refrain - from pensioners, who argue that CPI is falsely low because it over reflects the falling price of electronics but not the rocketing cost of heating bills and council tax; and from younger adults, who argue that it doesn't capture sky-high increases in house prices.