There is increased use and application of exponential random graphs emanating from use of big data and other techniques. This study sought to establish how sampling bias affects the exponential random graphs. This study was guided by the following objectives: to specify and estimate exponential random graph models with biased sampling, to determine the maximum likelihood estimate for family of exponential random graphs with sampling bias., to determine the suitable sampling method for exponential random graphs and to use the model effect in real life data; a case of opinion polls in Kenya. The study used R software for data analysis from IPSOS Synovate on opinion polls of 2017 in Kenya and realized that there is an intractable Pseudo likelihood for the family of exponential random graphs which was analyzed using the Markov Chain Monte Carlo simulation approach. The study revealed that gender and political affiliation affected the voting pattern of a person in an election at a rate 90.07% and 95.72% respectively. The study recommends use of Metropolis Hastings Monte Carlo simulation in handling the exponential random graphs.