You Light, She Lights, We All Light!
It is generally accepted in our countries1 that the most scrupulous practice2 is for each one in a household to light on the first night one candle. On the second (night) two candles, and so they add, until on the eigth night they are lighting eight. One should be careful that each person has their own special place for their candles, so that they will see how many candles each has lit. They should not light in a place where candles are lit during the rest of the year, so that it is obvious these are Hanukah lights.
1) This is the area around Hungary where Rabbi Shlomo Gantzfried, the compiler of the Kitzur, lived in the late 19th century CE.
2) In Talmud times, the ordinary people lit one candle per night per household, more strict people would have a menorah and light an extra candle each night, and only the most scrupulous would have a menorah for each member of the household. (KSA 139:6)